A car decreases its speed from 40 m/s to 20 m/s in 5 s. Find the acceleration of the car.
$-4 m/s^2$
Acceleration Calculation for a Changing Speed
This problem asks us to find the acceleration of a car when its speed changes over a specific period. Acceleration is the rate at which an object's velocity changes over time.
Understanding the Variables
- Initial Speed (\(u\)): The speed the car starts with. Here, \(u = 40\) m/s.
- Final Speed (\(v\)): The speed the car ends with. Here, \(v = 20\) m/s.
- Time (\(t\)): The duration over which the speed changes. Here, \(t = 5\) s.
- Acceleration (\(a\)): The value we need to find.
Formula for Acceleration
Acceleration is calculated using the formula:
\( a = \frac{v - u}{t} \)
Where:
- \(a\) is acceleration
- \(v\) is the final velocity
- \(u\) is the initial velocity
- \(t\) is the time interval
Step-by-Step Calculation
- Identify the given values:
- Initial speed, \(u = 40\) m/s
- Final speed, \(v = 20\) m/s
- Time, \(t = 5\) s
- Substitute the values into the acceleration formula:
\( a = \frac{20 \text{ m/s} - 40 \text{ m/s}}{5 \text{ s}} \)
- Calculate the change in speed:
\( v - u = 20 - 40 = -20 \text{ m/s} \)
The negative sign indicates that the speed is decreasing.
- Divide the change in speed by the time taken:
\( a = \frac{-20 \text{ m/s}}{5 \text{ s}} \)
- Determine the final acceleration value:
\( a = -4 \text{ m/s}^2 \)
Conclusion
The acceleration of the car is \( -4 \text{ m/s}^2 \). The negative sign signifies that the car is decelerating or slowing down.
Similar Questions
- Average Acceleration =
Important Questions from Acceleration
Acceleration is equal to the rate of change of _________.
At uniform speed the acceleration is
At uniform speed the acceleration is
- If the position of a particle X at time $t$ is given by the equation $x(t) = At^3$, where $A$ is a non-zero constant, determine the nature of its acceleration.
- Which of the following mathematical expressions accurately defines the average acceleration, $a$, of an object that changes its velocity from an initial velocity $v_i$ to a final velocity $v_f$ during a time interval $t$?
