Question

a) Write the formula for acceleration and give the meaning of each symbol which occurs in it.
b) A train starting from a railway station attains a speed of $21m{{s}^{-1}}$ in one minute. Find its acceleration.

Answer 1

Hint : Acceleration depends on the mass and also on the force. The force velocity, acceleration and momentum have both magnitude and a direction. Heavier objects have less acceleration compared to lighter objects. Three equations of motion of a uniformly accelerated object were derived by Newton's law of motion.

Complete step-by-step solution:
Acceleration is described as the rate of change of velocity of an object, irrespective of whether it speeds up or slows down. If it speeds up, acceleration is taken as positive and if it slows down, the acceleration is negative. It is caused by the net unbalanced force acting on the object, as per Newton's second law. Acceleration is a quantity as it describes the time rate of change of velocity and its SI unit is $m{{s}^{-2}}$ .
a) Acceleration is given by:
$Acceleration (a)=\dfrac{Final velocity(v)-Initial velocity(u)}{Time taken(t)}$
The above expression can be written as:
$a=\dfrac{v-u}{t}$
Velocity is defined as the rate of change of displacement with respect to time and in kinematics velocity is a fundamental concept.SI unit of velocity is $m{{s}^{-1}}$ velocity tracking is the measure of velocity.
Velocity (v) =$\dfrac{\Delta S}{\Delta t}$
The dimensional formula of velocity is ${{M}^{0}}{{L}^{1}}{{T}^{-1}}$.
b) From the data initial velocity ( $u$ ) =$0m{{s}^{-1}}$, final velocity ($v$ ) =$21m{{s}^{-1}}$ and Time ($t$ )=$1\min =60\sec$
$a=\dfrac{v-u}{t}$ $\cdots \cdots (1)$
After substituting
$a=\dfrac{21-0}{60}=0.35m{{s}^{-2}}$
$a=0.35m{{s}^{-2}}$

Note: The dimensional formula of displacement is ${{M}^{0}}{{L}^{1}}{{T}^{0}}$ and displacement plays a very important role while determining velocity (v). Velocity is also a vector quantity. Displacement plays a very important role while determining velocity (v). Displacement is a vector quantity which has both magnitude and direction and displacement is measured in terms of meters.