Question

A racing car is moving along a straight horizontal track with constant acceleration
there are 3 check points , P , Q , R on the track
where PQ = 48 m and QR = 200 m. The car takes 3 s to travel from P to Q and 5 s to travel from Q to R. Find
(i) the acceleration of the car ,
(ii) the speed of the car as it passes P.

Answer 1

Answer:

(i) 6m/s^2 , (ii)7m/s.

Explanation:

let the speed at P is v1 and acceleration is a.

s1 = 48m , t1 = 3s

s1 = v1t1 + 1/2×a(t1)^2

or, 48 = 3v1 + 9a/2

or, v1 = 16 - 3a/2

If the velocity of the car at Q = v2 , then

v2 = v1 + at1

or, v2 = 16 - 3a/2 + 3a = 16 + 3a/2

s2 = 200m , t2 = 5s

so, s2 = v2t2 + 1/2×a(t2)^2

or,200 = ( 16 + 3a/2 )5 + 25a/2

= 80 + 15a/2 + 25a/2

= 80 + 20a

or, a = 6m/s^2

v1 = 16 - (3×6)/2 = 16 - 9 = 7m/s.