A skier covers the final 110 meters of a race in 5.0 seconds

A skier covers the final 110 meters of a race in 5.0 seconds, crossing the finish line at a speed of 24 m/s. What was her (constant) acceleration?

The correct answer and explanation is :

The skier’s constant acceleration is 0.80 m/s².

Explanation:

We are given:

• The final distance covered: 110 m
• The time taken: 5.0 s
• The final velocity: 24 m/s

To find the constant acceleration, we use kinematic equations.

Step 1: Use the kinematic equation for displacement:

[
d = v_i t + \frac{1}{2} a t^2
]
where:

• ( d = 110 ) m,
• ( t = 5.0 ) s,
• ( v_i ) is the initial velocity,
• ( a ) is the acceleration.

Step 2: Use the velocity equation:

[
v_f = v_i + a t
]
where:

• ( v_f = 24 ) m/s.

Step 3: Solve for ( v_i ) and ( a )

We solve these two equations simultaneously:

1. ( 110 = v_i (5) + \frac{1}{2} a (5^2) ) → ( 110 = 5v_i + 12.5a )
2. ( 24 = v_i + 5a )

Solving these equations:

• ( v_i = 20 ) m/s (initial velocity)
• ( a = 0.80 ) m/s² (acceleration)

Thus, the skier’s acceleration is 0.80 m/s².

The plots above illustrate the skier’s motion:

1. Velocity vs. Time (Left Graph) – The skier’s velocity increases linearly over time due to the constant acceleration of 0.80 m/s².
2. Position vs. Time (Right Graph) – The distance covered follows a quadratic trend, as the skier’s speed increases over time.