Question

A car moves with a constant velocity of 10 m s^–1 for 10 s along a straight track, then it moves with uniform acceleration of 2 m s^–2 for 5 seconds. Find the total displacement and velocity at the end of 5th second of acceleration.​

Answer 1

Answer:

Let ${v_1}$ and ${t_1}$ be the initial velocity and time for the first part where the car is moving with a constant velocity.

${t_1}$ = 10 s; ${v_1}$ = 10 ms^–1

Therefore, distance travelled ${s_1}$

= ${v_1 t_1}$ = 10 × 10 = 100 m

For the second part i.e., when tje car accelerates,

a = 2 m s^–2, v = ?

t = 5 seconds

u = 10 m s^–1

v = u + at

v = 10 + 2 × 5

v = 10 + 10

v = 20 m s ^–1

${s_2}$ = ut + 1/2 at^2

= 10 × 5 + 1/2 × 2 × 5^2

= 50 + 1 × 25 = 50 + 25 = 75 m

Therefore, total displacement = 100 + 75

= 175 m.