Question

A car starts from rest and moves along the x axis with constant acceleration 5 metre per second square for 8 seconds if it then continues with constant velocity v distance will the car cover in 12 seconds since it started from rest

Answer 1

A car starts from rest (means initial velocity of the car is 0m/s) and moves along the x-axis with a constant acceleration 5m/s² for 8 second.

Using the First Equation Of Motion,

→ v = u + at

→ v = 0 + 5(8)

→ v = 40 m/s

Distance (s) covered by car = ut + 1/2 at²

→ s = 0(8) + 1/2 × 5 × (8)²

→ s = 0 + 1/2 × 5 × 64

→ s = 5 × 32

→ s = 160 m

We have to find the total distance covered by the car, if it continues with constant velocity v distance will the car cover in 12 seconds since it started from rest.

Remaining time = (12 - 8)sec = 4 sec

Now, time = 4 sec and velocity = 40 m/s.

So,

Distance covered by car in last 4 seconds,

Distance = Velocity × Time

→ 40 × 4 = 160 m

Total distance covered by car = (160 + 160)m = 320 m

Answer 2

GiveN :-

✪ initial velocity of the car, u = 0 m/s

(As it starts from rest)

✪ Acceleration, a = 5 m/s²

✪ Time, t = 8 s

TO FinD :-

The distance covered by the car when the time is 12 s since the start.

AcknowledgemenT :-

✪ v = u + at

• v is the final velocity (which is constant)
• u is the initial velocity
• a is the acceleration of the car
• t is the time taken

✪ v² - u² = 2as

• v is the final velocity (which is constant)
• u is the initial velocity
• a is the acceleration of the car
• s is the distance travelled

SolutioN :-

CASE-I

☛ Initial velocity(u) = 0 m/s

☛ Time(t) = 8 s

☛ Acceleration(a) = 5 m/s²

v = u + at

⇒v = 0 + 5(8)

⇒v = 40 m/s

v² - u² = 2as

⇒(40)² - (0)² = 2 × 5 × s

⇒1600 = 10s

⇒s = 160 m

$\rule{150}{2}$

CASE-II

Time is 12 s since the start. Distance travelled in 8 s since the start = 160 m. So, distance travelled in 12 s = distance travelled in 8 s + distance travelled in (12 - 8) s

Or

Distance travelled in 12 s = 160 m + Distance travelled in 4 s

Distance = Velocity × Time

⇒s = 40 × 4

⇒s = 160 m

Therefore, the car covers a distance of 160 m in 4 s.

Total distance covered by the car in 12 s = 160 + 160 = 320 m.