Question

True or False The speed of a particle at \(t=a\) is given by the value of the velocity at \(t=a\) . Justify your answer.

Short answer

False. The speed at time \(t=a\) is given by the absolute value of its velocity at \(t=a\), not the pure velocity value.

Step-by-step solution

Understanding the definitions

The speed of an object is a scalar quantity, or in other words, it does not have direction, all that matters is its magnitude. Velocity, on the other hand, is a vector quantity and is direction sensitive. It is also the rate of change of distance.

Analyze the statement

When we look at the statement that 'The speed of a particle at \(t=a\) is given by the value of the velocity at \(t=a\)', we conclude that since velocity can be both negative and positive due to its direction sensitivity, it does not always provide the speed of the particle. The correct statement should be 'The speed of a particle at \(t=a\) is given by the absolute value of the velocity at \(t=a\)'.