A cyclist and her bicycle have a combined mass of 70 kg. She accelerates from rest to a speed of 8.0 m/s. (a) Calculate the kinetic energy of the cyclist at...
Question 1 Report
A cyclist and her bicycle have a combined mass of 70 kg. She accelerates from rest to a speed of 8.0 m/s.
(a) Calculate the kinetic energy of the cyclist at 8.0 m/s. [2]
(b) The cyclist now doubles her speed to 16 m/s. Calculate her new kinetic energy. [1]
(c) State the factor by which KE increases when speed doubles. [1]
(d) Explain in terms of the equation for kinetic energy why doubling the speed more than doubles the kinetic energy. [2]
Answer Details
(a) Kinetic energy at 8.0 m/s [2]
Using \( KE = \tfrac{1}{2}mv^2 \):
\( KE = \tfrac{1}{2} \times 70 \times 8.0^2 = \tfrac{1}{2} \times 70 \times 64 \) [1]
\( KE = 2240 \text{ J} \) [1]
(b) Kinetic energy at 16 m/s [1]
\( KE = \tfrac{1}{2} \times 70 \times 16^2 = \tfrac{1}{2} \times 70 \times 256 = 8960 \text{ J} \) [1]
(c) Factor by which KE increases [1]
\( \dfrac{8960}{2240} = 4 \)
KE increases by a factor of 4 when speed doubles. [1]
(d) Why doubling speed more than doubles KE [2]
Kinetic energy depends on the square of the speed (\( v^2 \)) in the equation \( KE = \tfrac{1}{2}mv^2 \). [1]
When speed is doubled (multiplied by 2), \( v^2 \) is multiplied by \( 2^2 = 4 \). Since mass stays the same, KE also increases by a factor of 4, not 2. [1]
This is why high-speed collisions are so much more dangerous: a car travelling at 60 mph has four times the kinetic energy of one at 30 mph, requiring four times the braking distance (on a level road with constant braking force).
Download The App On Google Playstore
Everything you need to excel in your exams
