Motion - Kinematic Equations for Motion in a Straight

A racing car has a uniform acceleration of $4 \, m/s^2$. What distance will it cover in $10 \, s$ after start?

Given: Initial velocity $u = 0 \, m/s$ (starts from rest), Acceleration $a = 4 \, m/s^2$, Time $t = 10 \, s$. Using the second equation of motion: $s = ut + \frac{1}{2}at^2$ $s = (0 \times 10) + \frac{1}{2} \times 4 \times (10)^2$ $s = 0 + 2 \times 100$ $s = 200 \, m$

Since the car starts from rest, we set $u=0$. We use the position-time relation to find the distance covered in the given interval.

A train accelerating from $20 \, m/s$ reaches a speed of $50 \, m/s$ in $10 \, s$. Calculate the acceleration and the total change in velocity.

Initial velocity $u = 20 \, m/s$, Final velocity $v = 50 \, m/s$, Time $t = 10 \, s$. To find acceleration: $a = \frac{v - u}{t}$ $a = \frac{50 - 20}{10} = \frac{30}{10} = 3 \, m/s^2$ To find the change in velocity: $\begin{array}{r} 50 \\ -20 \\ \hline 30 \end{array}$ The change in velocity is $30 \, m/s$.

Acceleration is defined as the rate of change of velocity. We subtract the initial velocity from the final velocity and divide by the time interval.