Question

An object starting from rest travels 20 m in the first 2 s and 160 m in the next 4 s. What will be the velocity after 7 s from the start?

Answer 1

For first 2 s motion of object,

u = 0, f = 2 s, s = 20 m

Using s = `"ut" + 1/2 "at"^2`

we got 20 = `0 + 1/2 "a" xx 2^2`

or a = 10 ms⁻²

Velocity attained by object at the end of 2s

v = u + at 

= 0 + 10 × 2 

= 20 ms⁻¹

For next 4s, journey of object,

t' = 4s, u' = 20 ms⁻¹,  s' = 160 m

∴ s' = `"u'""t'" + 1/2 "a'""t'"^2`

⇒ 160 = `20 xx 4 + 1/2 xx "a'" xx 4^2`

or 8a' = 80 or a' = 10 ms⁻² 

It implies that acceleration is uniform throughout the journey.

∴ velocity after 7s from start, v = u + at

= 0 + 10 × 7 

= 70 ms⁻¹