The motion of a particle P moving a long a straight line is described by the equation s = 8t + 10t² – t³. Where...

The motion of a particle P moving a long a straight line is described by the equation s = 8t + 10t² – t³. Where s is the distance in metres and t is time in seconds.
Calculate:
(i) The distance when t = 2.5 sec.
(ii) The maximum velocity of the motion
(iii) The acceleration of motion after 3 seconds
(iv) The time at which the velocity is zero

---

---

sharon kalunda answered the question on August 20, 2019 at 12:40

Exams With Marking Schemes

• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Grade 9
• PP1
• PP2
• Playgroup
• Form 1
• Form 2
• Form 3
• Form 4

Related Questions

---

• The distance between two towns A and B is 460 km. A minibus left town A at 7:15 am and traveled towards B at an... (Solved)
  

  The distance between two towns A and B is 460 km. A minibus left town A at 7:15 am and traveled towards B at an average speed of 65 km/h.A car left B at 9:45 am on the same day and traveled towards A at an average speed of 100 km/h.
  (a) How far from B did they meet?
  (b) At what time did the two vehicles meet?
  (c) A motorist started from his home at 8:15 am on the same day and traveled to B at an average speed of 120 km/h. He arrived at the same time as the minibus. Calculate the distance from B to his home.

  Date posted: August 20, 2019 .    Answers (1)

• An open rectangular box measures externally 32cm long, 27cm wide and 15cm deep. If the box is made of wood 1cm thick, what volume of... (Solved)
  

  An open rectangular box measures externally 32cm long, 27cm wide and 15cm deep. If the box is made of wood 1cm thick, what volume of wood is used?

  Date posted: August 20, 2019 .    Answers (1)

• Use reciprocal tables to work out the following correct to 4s.f. (Solved)
  

  Use reciprocal tables to work out the following correct to 4s.f.
  

  Date posted: August 20, 2019 .    Answers (1)

• A cylindrical storage tank of diameter 14 cm is initially two thirds full of water. The tank is filled by a pipe of internal diameter... (Solved)
  

  A cylindrical storage tank of diameter 14 cm is initially two thirds full of water. The tank is filled by a pipe of internal diameter 10 cm through which water flows at the rate of 56 litres per minute. Water starts flowing into the tank at 10:15 am and the tank is full at 2:55 pm.
  (a) Determine the height of the tank.
  (b) Starting with the full tank, school uses water from this tank at the rate of 11,550 cm³ per day. Find how long it takes to consume all the water assuming that no more water is added.
  (c) How long does it take for the tap to fill the tank when empty?

  Date posted: August 20, 2019 .    Answers (1)

• A number of people working at a factory decided to raise sh. 72,000 towards a famine relief. Each person was to contribute the same amount.... (Solved)
  

  A number of people working at a factory decided to raise sh. 72,000 towards a famine relief. Each person was to contribute the same amount. Before the contributions were collected, five of the people retired from working at the factory. This means that the remaining contributors had to pay more to meet the same target.
  (a) Taking ‘n’ as the number of people working in the factory originally, write down an expression for the increase in the contribution per person.
  (b) If the increase in the contribution per person was sh. 1200, find the number of people originally.
  (c) How much would each person have contributed to the nearest shilling if the five had not retired?
  (d) Calculate the percentage increase in the contribution per person caused by retirements giving your answer to the nearest hundredth.

  Date posted: August 20, 2019 .    Answers (1)

• Using a ruler and a pair of compasses only, construct a triangle ABC such that AB = 6.3cm, BC = 4.5cm and angle ABC =... (Solved)
  

  Using a ruler and a pair of compasses only, construct a triangle ABC such that AB = 6.3cm, BC = 4.5cm and angle ABC = 120^o. Measure line AC.

  Date posted: August 20, 2019 .    Answers (1)

• Two grades of tea costing sh. 120 and sh. 150 per kilogram are mixed. In what ratio should the two grades be mixed in order... (Solved)
  

  Two grades of tea costing sh. 120 and sh. 150 per kilogram are mixed. In what ratio should the two grades be mixed in order to produce a mixture that costs sh. 144 per kilogram?

  Date posted: August 20, 2019 .    Answers (1)

• Three towns A, B and C are situated so that AB = 65 km and AC = 115 km. The bearing of B from A... (Solved)
  

  Three towns A, B and C are situated so that AB = 65 km and AC = 115 km. The bearing of B from A is 062^o and the bearing of C from A is 278^o.Calculate.
  a) The distance BC
  b) The bearing of B from C

  Date posted: August 20, 2019 .    Answers (1)

• Solve the following quadratic equations by completing the square method. 3x² – 7x – 5 = 0 (Solved)
  

  Solve the following quadratic equations by completing the square method.
  3x² – 7x – 5 = 0

  Date posted: August 20, 2019 .    Answers (1)

• The sum of the digits of a two digit number is 11. If the digits are interchanged the value of the number decreases by 63.... (Solved)
  

  The sum of the digits of a two digit number is 11. If the digits are interchanged the value of the number decreases by 63. What is the number?

  Date posted: August 20, 2019 .    Answers (1)

• The marked price of a pair of shoes is Sh. 2400. A customer buys the shoes and is offered a 10% discount and the seller... (Solved)
  

  The marked price of a pair of shoes is Sh. 2400. A customer buys the shoes and is offered a 10% discount and the seller still makes a profit of 20% on the cost of the shoes. Determine the cost price.

  Date posted: August 20, 2019 .    Answers (1)

• The figure below shows a uniform cross-section of a swimming pool which is 4m wide. The depth of the pool increase gently from 1.5m to... (Solved)
  

  The figure below shows a uniform cross-section of a swimming pool which is 4m wide. The depth of the pool increase gently from 1.5m to 3.0m.
  
  a) How much water in litres does it hold when full?
  b) Calculate total internal surface area of the pool.
  c) Find the angle at which the bottom of the pool inclines to the horizontal.

  Date posted: August 20, 2019 .    Answers (1)

• The diagram which is not drawn to scale, shows an isosceles triangle XYZ in which XY=YZ. The coordinates of x and y are (5,6) and... (Solved)
  

  The diagram which is not drawn to scale, shows an isosceles triangle XYZ in which XY=YZ. The coordinates of x and y are (5,6) and (0, -4) respectively.
  
  Given that the equation of line YZ is y=3/4x – 4 and that the perpendicular from X to YZ meet YZ at D,
  find.
  (i) The equation of XD
  (ii) The coordinate of D
  (iii) The coordinates of Z
  (iv) The area of triangle XYZ
  

  Date posted: August 20, 2019 .    Answers (1)

• Two airports are such that B is 500km due East of A. Two planes P and Q take off from A and B respectively and... (Solved)
  

  Two airports are such that B is 500km due East of A. Two planes P and Q take off from A and B respectively and at the same time. Place P flies at 360km/h on a bearing of 030^o. Plane Q flies at 240km/h on a bearing of 315^o. The two planes land after 90 minutes. Using a scale of 1:10,000,000:
  a) Show the positions of the planes after 90 minutes.
  b) Find the distance between the planes after 90 minutes.
  c) Find:
  (i) The bearing of plane P from plane Q after 90 minutes.
  (ii) The bearing of plane Q from plane P after 90 minutes

  Date posted: August 20, 2019 .    Answers (1)

• Mr. Biwott operates two passenger service vehicles along Nakuru- Eldoret route. One is a 16 seater Matatu and the other is 8-seater van. Each vehicle... (Solved)
  

  Mr. Biwott operates two passenger service vehicles along Nakuru- Eldoret route. One is a 16 seater Matatu and the other is 8-seater van. Each vehicle makes one route trip per day and the charges are ksh 250 and ksh 300 per passenger respectively (one way). The matatu uses diesel which costs ksh.48 per litre and the van uses regular petrol which costs ksh.52 per litre. The fuel consumption of the two vehicles is in the ratio of 4:3 respectively.
  a) If the matatu uses 80 litres for the round trip, determine the fuel consumption of the van for the round trip.
  b) Calculate the daily collection for each vehicle.
  c) Determine which vehicle is more profitable (on daily basis) and by how much.
  d) If the price of both types of fuel goes up by 20% determine the percentage change in daily collection.

  Date posted: August 20, 2019 .    Answers (1)

• The L.C.M of 15, 18 and a third number is 1260. Find the square of third number. (Solved)
  

  The L.C.M of 15, 18 and a third number is 1260. Find the square of third number.

  Date posted: August 20, 2019 .    Answers (1)

• Tap A takes one hour to fill a tank with water. If tap B takes y hours to remove the same water and both taps... (Solved)
  

  Tap A takes one hour to fill a tank with water. If tap B takes y hours to remove the same water and both taps takes 1 ½ hours to fill the tank, find the value of y.

  Date posted: August 20, 2019 .    Answers (1)

• Use reciprocal and cube root tables to evaluate. (Solved)
  

  Use reciprocal and cube root tables to evaluate.
  

  Date posted: August 20, 2019 .    Answers (1)

• Two points P and Q are found on the earth’s surface. The position of P is (52⁰S, 66⁰W) and Q (52⁰S, 114⁰E). Using earth’s radius... (Solved)
  

  Two points P and Q are found on the earth’s surface. The position of P is (52⁰S, 66⁰W) and Q (52⁰S, 114⁰E). Using earth’s radius = 6370km:
  
  (a) Find the difference in longitude between two points P and Q.
  
  (b) Calculate the shortest distance between points P and Q along:-
  (i) The Latitude in km (to 1 whole number).
  (ii) The Longitude in km (to one whole number).
  
  (c) A plane travelling at 800km/hr leaves point P at 10.00am and sails through South Pole to point Q. Find the local time the plane arrives at point Q to the nearest minutes.
  

  Date posted: August 20, 2019 .    Answers (1)

• The figure below represents a quadrilateral piece of land ABCD divided into three triangular plots. (Solved)
  

  The figure below represents a quadrilateral piece of land ABCD divided into three triangular plots. The lengths BE and CD are 100m and 80m respectively. Angle ABE = 30⁰, ACE = 45⁰ and ACD = 100⁰
  
  
  (a) Find to four significant figures:
  (i) The length of AE.
  (ii) The length of AD.
  (iii) The perimeter of the piece of land.
  
  (b) The plots are to be fenced with five strands of barbed wire leaving an entrance of 2.8m wide to each plot. The type of barbed wire to be used is sold in rolls of lengths 480m. Calculate the number of rolls of barbed wire that must be bought to complete the fencing of the plots.

  Date posted: August 20, 2019 .    Answers (1)