A cart maintains a constant velocity of 100 m/s for 10 seconds. During this interval its acceleration is

1. Break Down the Problem

We need to determine the acceleration of the cart while it maintains a constant velocity.

2. Relevant Concepts

• Definition of Acceleration: Acceleration is defined as the rate of change of velocity with respect to time.
• Formula: $a = \frac{\Delta v}{\Delta t}$ where $a$ is acceleration, $\Delta v$ is the change in velocity, and $\Delta t$ is the change in time.

3. Analysis and Detail

1. Identify the information given:

   • Initial velocity $v_i = 100 \, \text{m/s}$
   • Final velocity $v_f = 100 \, \text{m/s}$ (since the velocity is constant)
   • Time interval $\Delta t = 10 \, \text{s}$

2. Calculate Change in Velocity: $\Delta v = v_f - v_i = 100 \, \text{m/s} - 100 \, \text{m/s} = 0 \, \text{m/s}$

3. Apply the Formula for Acceleration: $a = \frac{\Delta v}{\Delta t} = \frac{0 \, \text{m/s}}{10 \, \text{s}} = 0 \, \text{m/s}^2$

4. Verify and Summarize

Since the cart is moving at a constant velocity, there is no change in velocity. Therefore, the calculated acceleration is correct and confirmed.

Final Answer

The acceleration of the cart is $0 \, \text{m/s}^2$.