Question

If a car at rest accelerates uniformly to a
speed of 144km/h in 20sec. Then it covers
a distance of​

Answer 1

Answer :

• The distance covered by the car at a uniform speed of 144 km/h in 20 s is 400 m.

Explanation :

Given :

• Final velocity of the car, v = 144 km/h or 40 m/s
• Initial velocity of the car, u = 0

[Here initial velocity is taken as 0 as the car has started from rest.]

• Time taken, t = 20 s

To find :

• The distance covered by the car, s = ?

Knowledge required :

⠀⠀⠀⠀→ First equation of motion :

⠀⠀⠀⠀⠀⠀⠀⠀v = u + at

Where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time Taken

⠀⠀⠀⠀→ Second equation of motion :

⠀⠀⠀⠀⠀⠀⠀⠀s = ut + ½at²

Where,

• s = Distance
• u = Initial velocity
• a = Acceleration
• t = Time taken

Solution :

First let us find the Acceleration of the car :

By using the First equation of motion and substituting the values in it, we get :

⠀=> v = u + at

⠀=> v = 0 + at

⠀=> v = at

⠀=> 40 = a(20)

⠀=> 40/20 = a

⠀=> 2 = a

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ a = 2 m/s²

Hence the accelaration of the car is 2 m/s².

Now,

Let's Find the distance traveled :

By using the second Equation of the motion and substituting the values in it, we get :

⠀=> s = ut + ½at²

⠀=> s = (0)t + ½at²

⠀=> s = ½at²

⠀=> s = ½ × 2 × 20²

⠀=> s = ½ × 2 × 400

⠀=> s = 400

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ s = 400 m

Therefore,

• The distance covered by the car, s = 400 m.

Answer 2

$\huge\underline{\pink{\bf Given :-}}$

• If a car at rest accelerates uniformly to a speed of 144 km/h in 20 sec

$\huge\underline{\pink{\bf To \: Find :-}}$

• Distance covered by the car

$\huge\underline{\pink{\bf Solution :-}}$

We have,

• Final Velocity(v) = 144 km/h = 40 m/s
• Initial Velocity(u) = 0 m/s
• Time taken(t) = 20 s

$\large\underline{\orange{\bf Step \: (1) :-}}$

In this step we have to find the acclaration of the car.

We know that,

$\boxed{\sf a = \dfrac{v - u}{t}}$

Where,

• a = Acceleration
• v = Final Velocity
• u = Initial Velocity
• t = Time taken

Substituting the given values we get,

➠ a = (40 - 0)/20

➠ a = (40)/20

➠ a = 2

∴ The acclaration of the car is $\sf 2 \: m/s^{2}$.

$\large\underline{\orange{\bf Step \: (2) :-}}$

In this step we have to find the distance covered by the car.

We know that,

$\boxed{\sf s = ut + \dfrac{1}{2}at^{2}}$

Where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• s = Distance covered

Substituting the given values we get,

➠ s = 0(20) + 1/2 × 2 × $\sf 20^{2}$

➠ s = 0 + 400

➠ s = 400

∴ The distance covered by the car is 400 m.