A car breaks from 360 km/h to a full stop in 10 s, what is its acceleration?
A. -10 m/s^2
B. -1 m/s
C. 1 m/s^2
D. 10 m/s^2
Answer (2)
The acceleration of the car is calculated to be -10 m/s², indicating deceleration as the car stops. This is derived from converting the speed from km/h to m/s and applying the acceleration formula. Thus, the answer is A. -10 m/s² .
;
Convert the initial velocity from km/h to m/s: 360 h km = 100 s m .
Use the formula for acceleration: a = t v f − v i .
Substitute the values: a = 10 0 − 100 .
Calculate the acceleration: a = − 10 s 2 m . The final answer is − 10 s 2 m .
Explanation
Convert Units First, we need to convert the initial speed from km/h to m/s. We know that 1 km is 1000 meters and 1 hour is 3600 seconds. Therefore, to convert km/h to m/s, we multiply by 3600 1000 .
Calculate Initial Velocity in m/s The initial velocity is 360 km/h. Converting this to m/s, we get: 360 h km = 360 × 3600 s 1000 m = 100 s m So, the initial velocity v i is 100 m/s. The final velocity v f is 0 m/s, and the time taken t is 10 s.
State the Formula for Acceleration Now we can calculate the acceleration using the formula: a = t v f − v i where:
a is the acceleration,
v f is the final velocity,
v i is the initial velocity,
t is the time taken.
Calculate the Acceleration Substituting the values, we get: a = 10 0 − 100 = − 10 s 2 m The acceleration is -10 m/s². The negative sign indicates that it is deceleration (the car is slowing down).
Final Answer Therefore, the acceleration of the car is -10 m/s².
Examples
Understanding acceleration is crucial in many real-world scenarios, especially in vehicle safety. For example, knowing the deceleration rate of a car helps engineers design effective braking systems. If a car can decelerate at a higher rate, it can stop in a shorter distance, potentially avoiding accidents. Similarly, understanding acceleration is important in designing trains, airplanes, and other modes of transportation to ensure passenger safety and comfort. In sports, athletes use acceleration to improve their performance, such as sprinters increasing their speed or baseball players hitting a ball harder.
