[tex] \underline{\underline{\large{\red{\mathcal{ ✒ GIVEN:}}}}} [/tex]
• The car starts at rest (the car was parked).
• The car reaches a speed of [tex]\rm{60 km/h}[/tex].
• The time it takes is [tex]\rm{5 \: s}[/tex]
[tex] \underline{\underline{\large{\red{\mathcal{REQUIRED:}}}}} [/tex]
Determine the acceleration.
[tex] \underline{\underline{\large{\red{\mathcal{SOLUTION:}}}}} [/tex]
Use the formula for [tex]\tt{\purple{average \: acceleration}}[/tex]
[tex]\boxed{\large{\bm{\red{a = \dfrac{ v_{f} - v_{0}}{t} }}}}[/tex]
[tex]\tt{Where;}[/tex]
[tex]\tt{v_{0}=}[/tex] is the initial velocity
[tex]\tt{ v_{f} =}[/tex] final velocity
[tex]\tt{t=}[/tex] time
In this case, since the car travels east throughout the motion, the velocity and the speed of the car are equivalent.
From the data give we know the initial speed is 0 m/s, the final speed is 60 km/h and the time is 5 s; before we can calculate the acceleration we need to transform the final velocity to m/s:
[tex]\tt{60 \frac{km}{h} \: \cdot \: \frac{1000m}{1km} \: \cdot \: \frac{1h}{3600} \approx 16.667}[/tex]
Hence, the final velocity is 16.667 m/s.
Now that we have the final velocity in the correct units we can find the acceleration:
[tex]\tt{a = \dfrac{16.667 - 0}{5} }[/tex]
[tex]\large{\tt{\purple{a \approx 3.33 }}}[/tex]
The acceleration is 3.33 m/s².
