Question

A scooter starts from rest moves in a straight line with a constant
acceleration and covers a distance of 64 m in 4s .(i) Calculate its
acceleration and final velocity. (ii) In how much time the scooter will
cover half the total distance?

Answer 1

Answer:

acceleration = 8m/s^2

final velocity = v = 32 m/s

ii) t = 2√2 sec

Explanation:

initial speed = u = 0 m/s

t = time = 4 s

s = distance = 64 m

i) s = ut + 1/2at^2

 64 = 1/2 * a * 16

a = 8 m/s^2

   v = u+at

     = 8 * 4 = 32 m/s

ii) half distance = 32 m

s = ut + 1/2at^2

32 = 1/2 * 8 * t^2

8 = t^2

t = 2√2 sec

Answer 2

Answer:

(i) a = 8 m/s² , v = 32 m/s (ii) 2√2 s

Explanation:

Given,

(i) For acceleration

s = 64m

u = 0 m/s (starts from rest)

t = 4s

From second equation of motion,

s = ut + 1/2 (at²)

64 = 0t + 1/2 (a)(4)(4)

64 = 8a

a = 8 m/s²

For final velocity,

From first equation of motion,

v = u + at

v = 0 + (8)(4)

v = 32 m/s

(ii)

We have to find the time the scooter takes to cover half the distance

= s/2 = ut + 1/2 (at²)

32 = 0t + 1/2 (8)(t²)

32 = 4t²

8 = t²

√8 = t

2√2 s = t