A body is moving according to the equation $x = at + b{t^2} - c{t^3}$ where $x = $ displacement and $a,\;b$ and $c$ are constants. The acceleration of the body is

What will be change in speed of moving object if both speed and acceleration are positive or negative ?

A body starts with an initial velocity of $10\,ms ^{-1}$ and is moving along a straight line with constant acceleration. When the velocity of the particle is $50\,ms ^{-1}$, the acceleration is reversed in direction. The velocity of the particle when it again reaches the starting point is $............\,m/s^{-1}$

The area under acceleration-time graph gives

Stopping distance of vehicles : When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity $(v_0)$ and the braking capacity, or deceleration, $-a$ that is caused by the braking. Derive an expression for stopping distance of a vehicle in terms of $v_0 $ and $a$.

A particle starts from rest, accelerates at $2 \,ms^{-2}$ for $10\,s$ and then goes for constant speed for $30\,s$ and then decelerates at $ 4\, ms^{-2}$ till it stops. What is the distance travelled by it.........$m$