College

Select the correct answer.

Sully is riding a snowmobile on a flat, snow-covered surface with a constant velocity of 10 meters/second. Sully's total mass is 280 kilograms. If Sully accelerates to a velocity of 16 meters/second over 10 seconds, what is the force required to accelerate? Use [tex]$F=ma$[/tex], where [tex]$a=\frac{v-u}{t}$[/tex].

A. 160 N
B. 168 N
C. 248 N
D. 280 N
E. 324 N

Answer :

Sure! Let's break down the problem and solve it step by step to find the correct answer.

1. Identify the given information:

- Initial velocity ([tex]\( u \)[/tex]) = 10 meters/second
- Final velocity ([tex]\( v \)[/tex]) = 16 meters/second
- Time taken ([tex]\( t \)[/tex]) = 10 seconds
- Mass of Sully and the snowmobile ([tex]\( m \)[/tex]) = 280 kilograms

2. Calculate the acceleration ([tex]\( a \)[/tex]):

Acceleration is calculated using the formula:
[tex]\[
a = \frac{v - u}{t}
\][/tex]

Substituting the given values:
[tex]\[
a = \frac{16 \, \text{m/s} - 10 \, \text{m/s}}{10 \, \text{s}} = \frac{6 \, \text{m/s}}{10 \, \text{s}} = 0.6 \, \text{m/s}^2
\][/tex]

3. Calculate the force ([tex]\( F \)[/tex]):

Force is calculated using the formula:
[tex]\[
F = m \times a
\][/tex]

With the mass ([tex]\( m \)[/tex]) and acceleration ([tex]\( a \)[/tex]) we found:
[tex]\[
F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N}
\][/tex]

Therefore, the force required is [tex]\( 168 \, \text{N} \)[/tex], which corresponds to option B.