Question

Acceleration of a particle starting from rest is a = = (5t) ms
then its velocity at t = 2s is
(A) 5 ms
-1
(B) 10 ms 1
(C) 15 ms-1
(D) 20 ms-1​

Answer 1

Proper question: Acceleration of a particle starting from rest is 5 m/s² then its velocity at time = 2 seconds!?

Provided that:

• Initial velocity = 0 m/s
• Time = 2 seconds
• Acceleration = 5 m/s²

Don't be confused! Initial velocity cames as zero because the particle starts from the rest.

To calculate:

• The final velocity

Solution:

• The final velocity = 10 m/s

Using concept:

• Acceleration formula

Using formula:

• ${\small{\underline{\boxed{\sf{a \: = \dfrac{v-u}{t}}}}}}$

Where, a denotes acceleration, v denotes final velocity, u denotes initial velocity and t denotes time taken.

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time \: taken} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf 5 \: = \dfrac{v-0}{2} \\ \\ :\implies \sf 5 \: = \dfrac{v}{2} \\ \\ :\implies \sf 5 \times 2 \: = v \\ \\ :\implies \sf 10 \: = v \\ \\ :\implies \sf v \: = 10 \: ms^{-1} \\ \\ :\implies \sf Final \: velocity \: = 10 \: ms^{-1}$

The final velocity is 10 m/s, therefore, option B) is absolutely correct!