Question

A red cart starts from rest at the top of a ramp and coasts down the ramp with a constant acceleration. A blue motor car starts at the top of the same ramp directly beside the red cart. The blue motor car moves down the ramp with a constant speed.
When the red cart catches up to the blue car, how does the speed of the red cart compare with the speed of the blue car?

• A. The red cart is moving at the same speed as the blue car
• B. The red cart is moving slightly faster than the blue car
• C. The red cart is moving more slowly than the blue car
• D. The red cart is moving twice as fast as the blue car

Answer 1

Answer: (D)

The red cart is moving twice as fast as the blue car

Distance traveled by red cart=$\frac{1}{2}a{t}^2$

Distance traveled by blue cart=$vt$

When the two carts meet,

$\frac{1}{2}a{t}^2=vt$

$⟹t=\frac{2v}{a}$

The speed of red cart on meeting=$at=2v$

The speed of blue cart remains the same and equal to $v$.

Hence correct answer is option D.