Question

If one object has a greater speed than a second object, does the first necessarily have a greater acceleration? Explain, using examples.

Short answer

No, because there is no relationship between the magnitude of speed and the magnitude of acceleration.

Step-by-step solution

Step 1. Meaning of acceleration

Acceleration is the rate at which an object changes its velocity. It has both direction and magnitude, and its value can be positive, negative, or zero.

Step 2. Examples for explaining the given condition

An object can have a large speed with constant velocity. In this case, its acceleration remains zero. An object can also have a small speed but with gain. In this case, its acceleration is positive.

Here, the object with the greater speed has lesser acceleration.

Consider two objects are dropped from rest at different times. By ignoring air resistance, the object dropped first has a greater speed than the second one, but both have the same acceleration.