Select the correct answer.

Sully is riding a snowmobile on a flat, snow-covered surface with a constant velocity of 10 meters/second. Sully and the snowmobile together have a mass of 280 kilograms. If Sully accelerates to a velocity of 16 meters/second over 10 seconds, use [tex]F = ma[/tex], where [tex]a = \frac{v - u}{t}[/tex].

A. [tex]160 N[/tex]
B. [tex]168 N[/tex]
C. [tex]248 N[/tex]
D. [tex]280 N[/tex]
E. [tex]324 N[/tex]



Answer :

Sure, let's break down the problem step-by-step:

1. Given Data:
- Mass of Sully on the snowmobile, [tex]\( m = 280 \)[/tex] kg
- Initial velocity, [tex]\( u = 10 \)[/tex] m/s
- Final velocity, [tex]\( v = 16 \)[/tex] m/s
- Time taken for acceleration, [tex]\( t = 10 \)[/tex] seconds

2. Calculate Acceleration:

The acceleration can be calculated using the formula:
[tex]\[ a = \frac{v - u}{t} \][/tex]
Plug in 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 Force:

Now we can calculate the force using the formula [tex]\( F = ma \)[/tex]:
[tex]\[ F = 280 \text{ kg} \times 0.6 \text{ m/s}^2 = 168 \text{ N} \][/tex]

So, the force required is [tex]\( 168 \ \text{N} \)[/tex].

Given the options provided, the correct answer is:
- B. [tex]\( 168 \text{ N} \)[/tex]