Question

A body starting with a velocity v returns to its initial position after t second with the same speed along the same line. Acceleration of the particle is:

Answer 1

Hint: Given body is starting with v; this gives initial velocity is v, time taken is t. The body returns to its initial velocity with the same speed. Then, final velocity is negative of v. We have to find the acceleration of the particle; it can be obtained using first equation of motion.

Complete step-by-step solution:
Distance covered by the traveling body per unit of time provides the measure of the object's velocity. It says about how far a body moves in a provided interval of time. Acceleration is the change of velocity with the time of an object concerning time. Like velocity, it is a vector holding both acceleration and magnitude
Given: A body starting with a velocity v, it means we have given initial velocity v.
Time taken t is given.
Body returns to its initial position with the same speed along the same line, it means final velocity is $-v$.
Using the first equation of motion, we can find the acceleration.
$v = u + at$
Where v is final velocity.
u is initial velocity.
t is time taken.
a is acceleration.
Put all values, we get:
$v = v + at$
$\implies -2v = at$
$\implies a = \dfrac{-2v}{t}$
Hence, acceleration is $\dfrac{-2v}{t}.$

Note: When an object covers a straight line with an increment in velocity at regular periods; then, the object is in uniform acceleration. When an object moves with an increment in velocity but not at regular intervals of time is named non-uniform acceleration. The object's acceleration at any instant of time is identified as instantaneous acceleration.