The unit of acceleration is $m\,{s^{ - 2}}$ (metres per second squared). The sprinter might have an acceleration of $5m\,{s^{ - 1}}$; her velocity increases by $5m\,{s^{ - 1}}$ every second. You could express acceleration in other units.
For example, an advertisement might claim that a car accelerates from 0 to 60 miles per hour (mph) in 10 s. Its acceleration would then be 6 mph ${s^{ - 1}}$ (6 miles per hour per second). However, mixing together hours and seconds is not a good idea, and so acceleration is almost always given in the standard SI unit of $m\,{s^{ - 2}}$
WORKED EXAMPLES
1) Leaving a bus stop, a bus reaches a velocity of $8.0\,m\,{s^{ - 1}}$ after $10 s$. Calculate the acceleration of the bus.
Step 1: Note that the bus’s initial velocity is $0\,m\,{s^{ - 1}}$.
Therefore:
${\rm{change in velocity}}\,\Delta v = (8.0 - 0)\,m\,{s^{ - 1}}$
$time\,taken\,\Delta t = 10s$
Step 2: Substitute these values in the equation for acceleration:
$\begin{array}{l}
acceleration = \frac{{\Delta v}}{{\Delta t}}\\
= \frac{{8.0}}{{10}}\\
= 0.80\,m\,{s^{ - 2}}
\end{array}$
2) A sprinter starting from rest has an acceleration of $5.0\,m\,{s^{ - 1}}$ during the first $2.0 s$ of a race.
Calculate her velocity after $2.0 s$.
Step 1: Rearranging the equation $a = \frac{{v - u}}{t}$ gives:
$v = u + at$
Step 2: Substituting the values and calculating gives:
$v = 0 + (5.0 \times 2.0) = 10\,m\,{s^{ - 1}}$
3) A train slows down from $60\,m\,{s^{ - 1}}$ to $20\,m\,{s^{ - 1}}$ in $50 s$. Calculate the magnitude of the deceleration
of the train.
Step 1: Write what you know:
$u = 60\,m\,{s^{ - 1}}\,\,\,\,\,\,\,\,\,v = 20\,m\,{s^{ - 1}}\,\,\,\,\,\,\,\,\,t = 50s\,$
Step 2: Take care! Here the train’s final velocity is less than its initial velocity. To ensure that we arrive at the correct answer, we will use the alternative form of the equation to calculate a.
$\begin{array}{l}
a = \frac{{v - u}}{t}\\
= \frac{{20 - 60}}{{50}} = \frac{{ - 40}}{{50}}\\
= - 0.80\,m\,{s^{ - 2}}
\end{array}$
The minus sign (negative acceleration) indicates that the train is slowing down. It is decelerating. The magnitude of the deceleration is $0.8\,m\,{s^{ - 2}}$.
1) A car accelerates from a standing start and reaches a velocity of $18\,m\,{s^{ - 1}}$ after $6.0 s$. Calculate its acceleration.
2) A car driver brakes gently. Her car slows down from $23\,m\,{s^{ - 1}}$ to $11\,m\,{s^{ - 1}}$ in $20 s$. Calculate the magnitude (size) of her deceleration. (Note that, because she is slowing down, her acceleration is negative.)
3) A stone is dropped from the top of a cliff. Its acceleration is $9/81\,m\,{s^{ - 2}}$. How fast is it moving:
after $1.0 s$?
after $3.0 s$?
