Question

A particle that is moving along a straight line decelerates uniformly from 40 cm/s to 20 cm/s in 5.0 s and then has a
constant acceleration of 20 cm/s2
during the next 4.0 s. The average speed over the whole time interval is

Answer 1

Given info : A particle that is moving along a straight line decelerates uniformly from 40 cm/s to 20 cm/s in 5.0 s and then has a  constant acceleration of 20 cm/s² during the next 4.0s.

To find : the average speed over the whole time interval is ...

solution : case 1 : initial velocity, u = 40 cm/s

final velocity, v = 20 cm/s

time taken, t =  5sec

using formula, v = u + at

⇒ 20 cm/s = 40 cm/s + a × 5sec

⇒ a = - 4 cm/s²

now distance covered by the particle is, s₁ = ut + 1/2 at²

    = 40 cm/s × 5sec + 1/2 × -4cm/s² × (5sec)²

    = 200 cm - 50 cm = 150 cm

case 2 : initial velocity, u = 20 cm/s ,

acceleration, a = 20 cm/s²

time taken, t = 4 sec

using formula, s = ut + 1/2at²

⇒ s₂  = 20 × 4 + 1/2 × 20 × 4² = 80 + 160 = 240 cm

∵ average speed = total distance/total time taken

                             = (150 cm + 240 cm)/(5sec + 4sec)

                             = 390 cm/9 sec = 43.33 cm/s

therefore the average speed over the whole time interal is 43.33 cm/s.