Question

A car moves in a straight line from rest at t=0. It accelerates with 2m/s^2.
Displacement= 25m, find time and velocity.

Answer 1

Answer:

• Time = 5 secs
• Velocity = 10 m/s

Explanation:

Given that ;

Initial velocity (u) = 0

Acceleration (a) = 2 m/s²

Displacement(s) = 25 m

We will use equation of motion :

v² - u² = 2as

⇒ v² - 0 = 2 * 2 * 25

⇒ v² = 100

⇒ v² = (10)²

⇒ v = 10 m/s

Hence, the velocity of the car is 10 m/s.

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Again, using equation of motion ;

v = u + at

⇒ 10 = 0 + 2 * t

⇒ 10 = 2t

⇒ t = $\sf \dfrac{10}{2}$

⇒ t = 5 secs

_______________________

Hence, the time take by car is 5 secs and the velocity acquired is 10 m/s.

Answer 2

Solution :-

As provided :-

▪️Initial velocity = 0

▪️Acceleration = 2 m/s²

▪️Displacement = 25 m

Now we have got the Displacement , acceleration and the time.

So we can use the Motion equation :-

S = ut + 1/2 at²

→ 25 = 0(t) + 1/2 × 2 × t²

→ 25 = t²

→ t = ±5

But as time can never be negative

So the time taken = 5 sec

Now we have to find out the velocity .

We have got two methods for finding out Velocity .

1. v = u + at

2. v² = u² + 2aS

So by First Method :-

v = u + at

→ v = 0 + 2(5)

→ v = 10 m/s

By using second method :-

v² = u² + 2aS

→ v² = 0² + 2(2)(25)

→ v² = 0 + 100

→ v² = 100

→ v = ± 10

But as acceleration was positive

→ v = 10 m/s

So

$\huge{\boxed{\sf{ Time = 5 \: sec}}}$

$\huge{\boxed{\sf{Velocity = 10 \: m/s}}}$