Question

A car starts from rest and accelerates uniformly at 7 m/s^2. Calculate the speed after 13 seconds.

Answer 1

Provided that:

• Initial velocity = 0 mps
• Acceleration = 7 mps sq.
• Time = 13 seconds

Don't be confused! Initial velocity cames as zero because the body starts from rest.

To calculate:

• Final velocity

Solution:

• Final velocity = 91 mps

Using concept(s):

• To solve this question we can use either first equation of motion or acceleration formula.

• Choice may vary!

Using formulas:

• The first equation of motion:

• ${\small{\underline{\boxed{\pmb{\sf{v \: = u \: + at}}}}}}$

• Acceleration formula:

• ${\small{\underline{\boxed{\pmb{\sf{a \: = \dfrac{v-u}{t}}}}}}}$

Where, a denotes acceleration, u denotes initial velocity, v denotes final velocity and t denotes time taken.

Required solution:

~ Let us calculate the final velocity!

By using acceleration formula...

»»» a = (v-u)/t

»»» 7 = (v-0)/13

»»» 7 = v/13

»»» 7 × 13 = v

»»» 91 = v

»»» v = 91 mps

»»» Final velocity = 91 mps

By using first equation of motion...

»»» v = u + at

»»» v = 0 + 7(13)

»»» v = 0 + 91

»»» v = 91 mps

»»» Final velocity = 91 mps

• Henceforth, the speed after 13 seconds = 91 mps! $\:$

Additional information:

• The three equations of motion:

$\begin{gathered}\boxed{\begin{array}{c}\\ {\pmb{\sf{Three \: equation \: of \: motion}}} \\ \\ \sf \star \: v \: = u \: + at \\ \\ \sf \star \: s \: = ut + \: \dfrac{1}{2} \: at^2 \\ \\ \sf \star \: v^2 - u^2 \: = 2as\end{array}}\end{gathered}$