Question

distance travelled by a body is given by 2s=(10t+5t^2)m.the acceleration of the body is

Answer 1

Answer:

Distance travelled by a body is given by 2s=(10t+5t^2)m.the acceleration of the body is. 2. See answers.

Answer 2

Answer:

The acceleration of the body is 5m/s².

Explanation:

Given the distance travelled by a body,

$2s=(10t+5t^2)m$

Rewriting the equation,

$s=\dfrac{10t+5t^2}{2} m$

Velocity of a body is defined as the rate of change of displacement, and is given by

$v=\dfrac{ds}{dt}$

where s is the displacement and t is the time

Acceleration of the body is defined as the rate of change of velocity, and is given by

$a=\dfrac{dv}{dt}$

where v is the velocity.

Substituting the velocity, $v=ds/dt$, the acceleration can be written as

$a=\dfrac{d}{dt} \bigg(\dfrac{ds}{dt} \bigg)=\dfrac{d^2s}{dt^2}$

Thus, the acceleration of the body given is

$\dfrac{d^2}{dt^2}\bigg(\dfrac{10t+5t^2}{2} \bigg)=\dfrac{d}{dt}\bigg(\dfrac{d}{dt}\dfrac{10t}{2}+ \dfrac{d}{dt}\dfrac{5t^2}{2}\bigg)$

                         $=\dfrac{d}{dt}\bigg(\dfrac{10}{2}+ \dfrac{10t}{2}\bigg)$

                         $=\dfrac{d}{dt}\bigg(\dfrac{10}{2}\bigg)+ \dfrac{d}{dt}\bigg(\dfrac{10t}{2}\bigg)$

                         $= \dfrac{10}{2}=5m/s^2$

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

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