calculate the distance traveled by the particle during the 2 nd second. (4 mks) 1. A particle moves such that t seconds after passing a given point O , its distance S metres from O is given by S= t (t-2) (t-1) (a) Find its velocity when t = 2 seconds (b) Find its minimum velocity (c)Find the time when the particle is momentarily at rest (d) Find its acceleration when t = 3seconds x-axis y-axis 2 4 6 8 10 12 14 4 0 8 12 16 20 24 28
2. The table below gives the values of x and y for the curve y=x 2 +1 X 0 1 2 3 4 5 6 7 8 9 10 y 1 2 10 17 37 50 82 a) Complete the table b) Use the mid- ordinate rule to estimate the area enclosed by the curve y = x 2 + 1. Use five coordinates c) Using integration, calculate the actual area in (a) above d) Calculate the percentage error in the estimated area 3. The gradient function of a curve is given by the expression 2x + 1 . If the curve passes through the point (-4, 6); find the equation of the curve 4. A particle P moves in a straight line so that its velocity, Vm/s at time t seconds where t 0 is given by v = 28 + t – 2t 2 Find; (a) the time when P is instantaneously at rest (b) the speed of P at the instant when the acceleration of P is zero (c) Find the acceleration of P when the article is instantaneously at rest (d) Find the distance covered by the particle during the 3 rd second, when at t = 0 D = 5M 5. A particle K moves a long a straight line 50 cm long. At time t = 0, k is at A and t seconds later its velocity vcm/s is given by v = 15 + 4t – 3t 2 . a) Write down the expression for; i) The acceleration of K at time t seconds. ii) The distance of K from A at time t seconds. b) i) Find t when K is instantaneously at rest. ii) How far is K from A at this time? c) Find the period of time during which the acceleration of P is positive. 6. The diagram below shows the sketch of the curve y = x 2 and y = -x 2 + 8 intersecting at A and B :- (a) Find the value of a and b hence find the coordinates of A and B (b) Find the area enclosed by x = a, x = b , the axis and:- (i) the curve y = x 2 (ii) the curve y = -x + 8 7. The distance from a fixed point of a particle in motion at any time t seconds is given by :- S = t 3 – 5 / 2 t 2 + 2t + 5 metres Find its: (a) Acceleration after t seconds (b) Velocity when acceleration is zero 8 A particle moves in a straight line. It passes through point O at t = 0 with a velocity v = 5 m/s. The acceleration a m/s 2 of the particle at time t seconds after passing through O is given by a = 6t + 4 (a) Express the velocity v of the particle at time t seconds in terms of t. (b) Calculate the velocity of the particle when t = 4. (c) (i) Express the displacement s by the particle after t seconds in terms of t . (ii) Calculate the distance covered by the particle between t = 1 and t = 4. y A a b B O x
9 . The displacement S metres of a particle moving along a straight line after t seconds is given by. S = 3t + 3t 2 – 2t 3 2 a) Find its initial acceleration b) Calculate: i) The time when the particle was momentarily at rest ii) Its displacement by the time it came to rest momentarily c) Calculate the maximum speed attained 10. Find the equation to the tangent to the curve:- y = 4x 3 – 2x 2 – 3x + 5 at the point (2, 23) 11. A farmer wanted to make a trough for cows to drink water. He had a metal sheet measuring
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