by Mr Teh DEC 2010

topic 17: Kinematics “A stupid question is the one not asked”

E: maths.w.mr.teh@gmail.com ~ 1 ~ If you find this useful, CALL

+65-9832 2013 and ask for MORE

Question 1:

A particle starts from rest from a point O and moves in a straight lines

such that its velocity, v cm/s, is given by 2

22ttv −= , where t is the

time in seconds after the start of its motion. Calculate

(a) the maximum velocity of the particle, (b) its acceleration when the particle is instantaneously at rest, (c) the value of t when the particle returns to O, (d) the distance travelled in the first 6 seconds.

Question 2:

A particle moves in a straight line so that its distance s metres from a fixed point O at time t seconds is given by the formula

296 23 −+−= ttts . Find

(a) the initial velocity of the particle, (b) the time(s) when the particle is instantaneously at rest, (c) the total distance travelled in the interval 50 ≤≤ t .

Question 3:

An object moves in a straight line and its displacement, s metres, from

a fixed point O is given by ttts 107 23 +−= , where t is the time in

seconds after passing O. Find the

(a) speed after 2 seconds, (b) acceleration after 4 seconds, (c) times when the object is momentarily at rest, (d) values of t when the object returns to O.

Question 4:

A particle moving in a straight line passes a fixed point O with a velocity of 15 m/s. Its acceleration, a m/s2 is given by ta 47 −= , where t is the time in seconds after passing O. Find

(a) the maximum speed reached by the particle in the original direction of the motion,

(b) the value of t when the particle is instantaneous at rest, (c) the displacement of the particle from O when t = 6 seconds, (d) the average speed of the particle during the first 6 seconds.

Question 5:

A particle travels in a straight line so that, t s after passing a fixed point O, its speed, 1ms −v , is given by 52 ++= pttv where p is a constant.

It is given that its acceleration at time 5 seconds is 2ms 4 − and that it comes to instantaneous rest at points A and B, situated along the straight line. (a) Find the value of p. (b) Find the time it reaches points A and B respectively, (c) Find the distance between points A and B. (d) Sketch the velocity-time graph for 60 ≤≤ t and find the range of

time when the particle experiences deceleration.

by Mr Teh DEC 2010

topic 17: Kinematics “A stupid question is the one not asked”

E: maths.w.mr.teh@gmail.com ~ 2 ~ If you find this useful, CALL

+65-9832 2013 and ask for MORE

Question 6:

A particle P moves in a straight line so that its velocity, 1ms −v , is given

by 1072 +−= ttv , 0≥t , where t is the time in seconds after leaving a point A which is 2 m away from a fixed point O.

(a) Find an expression, in terms of t, for (i) the acceleration of P, (ii) the distance of P from O.

(b) Find (i) the distance from O of the point where P first comes

instantaneously to rest, (ii) the average speed of P during the first 3 seconds.

Question 7:

A particle moves in a straight line and passes a fixed point O with a

velocity, v m/s, given by 12112 2 −+−= ttv , where t seconds is the time after passing O. Find

(a) the times when the particle is momentarily at rest, (b) the total distance travelled in the first 5 seconds, (c) the maximum velocity of the particle.

Question 8:

A particle moves in a straight line so that t seconds after passing

through O, its velocity 1cms −v , is given by 562 +−= ttv . The particle comes to instantaneous rest, firstly at A and then at B. Find

(a) the velocity of the particle when its acceleration is zero, (b) an expression, in terms of t, for the distance of the particle from O

at time t, (c) the distance AB, (d) the total distance travelled in the first 8 seconds after passing

through O.

Question 9:

A particle moves in a straight line so that t seconds after passing

through O, its velocity, 1ms −v is given by 672 +−= ttv . The particle comes to instantaneous rest, firstly at P and then at Q. Find

(a) an expression for the displacement, s m, of the particle from O at time t,

(b) the distance PQ. (c) Given that R is the point at which the particle has zero acceleration,

determine, with working, whether R is nearer to Q or to O.

by Mr Teh DEC 2010

topic 17: Kinematics “A stupid question is the one not asked”

E: maths.w.mr.teh@gmail.com ~ 3 ~ If you find this useful, CALL

+65-9832 2013 and ask for MORE

Question 10:

A particle moves in a straight line from a point O such that, t seconds

after leaving O, its velocity 1ms −v , is given by )1(10 tev −−= . Calculate

(i) the acceleration of the particle when t = 2, (ii) the displacement of the particle from O when t = 2, (iii) the maximum possible velocity that the particle will tend to attain

when t is very large.