XMS AMATH Kinematics practice

Xinmin Secondary School Additional Mathematics [401] Topic: Kinematics Name: ______________________________ ( ) Date: ___________ Complete all questions on writing paper. Question 1 A particle starts from point O and moves in a straight line with a velocity, 1s m −v , given by 152 2 ++−= ttv , where t seconds is the time after leaving O. Calculate (a) the acceleration of the particle when it is instantaneously at rest, (b) the initial acceleration, (c) the total distance travelled by the particle from 2=t to 6=t . Answer (a) 2s m 11 −− (b) 2s m 1 − (c) m 3 172 Question 2 A particle starts moving in a straight line, with a displacement of 3 m away from a fixed point O. The velocity, 1s m −v , of the particle t seconds after the start of its motion, is given by tev 24−= . Find (a) the initial acceleration of the particle, (b) the time when the particle is instantaneously at rest, (c) the total distance travelled by the particle in the first 2 seconds, correct to 3 significant figures. Answer (a) 2s m 2 −− (b) (ln 2) s (c) 21.3 m Question 3 A particle moves in a straight line such that its distance from a fixed point O, t seconds after leaving O, is given by tts 2cos223 +−= . Find (a) the velocity and acceleration of the particle in terms of t, (b) the time when the particle is first instantaneously at rest, correct to 3 significant figures, (c) the distance travelled by the particle in the first second of motion, correct to 3 significant figures Answer (a) tatv 2cos8;2sin43 −=−= (b) s 424.0 (c) 1.02 units