Question

A car starts from rest and accelerates uniformly over a time of 6 seconds for a distance of 90 m. Determine the acceleration of the car,​

Answer 1

Given :-

▪ A car starts from rest and accelerate uniformly over a time of 6 seconds for a distance of 90 m.

To Find :-

▪ Acceleration of the car.

Solution :-

Given us the initial velocity, time taken and the Distance travelled, Using the Newton's second Equation of motion, acceleration can be calculated as,

⇒ s = ut + 1/2 at²

⇒ 90 = 0×6 + 1/2 × a × 6²

Because the car was at rest, so the initial velocity will be 0 m/s

⇒ 90 = 36/2 a

⇒ 90 = 18 a

⇒ a = 90 / 18

⇒ a = 5 m/s²

Hence, The acceleration of the car is 5 m/s².

Some Information :-

☞ Newton's equations of motion are applied when:

• No presence of external forces.
• No Friction.
• Acceleration must be uniform.

There are three equations of motion :-

• v = u + at
• s = ut + 1/2 at²
• 2as = v² - u²

Where,

• u = Initial velocity
• v = final velocity
• t = Time taken
• a = Acceleration
• s = Displacement

Answer 2

Given : A car starts from rest and accelerates uniformly over a time of 6 seconds for a distance of 90 m.

　

To find : Determine the acceleration of the car.

　

Using formula :

[Using second equation of motion].

★ s = ut + 1/2 at².

　

Calculations :

→ 90 = 0 (6) + 1/2 (a) (6)²

→ 90 = 36/2 (a)

→ a = 90/18

→ a = 5 m/s²

　

Or

　

→ Acceleration = 2 (90)/6²

→ Acceleration = 180/6²

→ Acceleration = 5 m/s²

　

Therefore, 5 m/s² is the acceleration of the car.