Question

A cart moves toward a motion sensor on a track in three different ways: speeding up with constant speed slowing to a stop and turning around to speed up in the opposite direction For each of these cases, what is the sign of the velocity and what is the sign of the acceleration at the beginning of the trip and at the end of the trip?

Answer 1

Acceleration of the cart in the beginning is positive

Speed is positive when speeding up and slowing down.

Speed is zero when the cart stops.

Speed is negative when the cart speeds up in opposite direction.

Acceleration is negative when speeding up in opposite direction from rest.

Step-by-step explanation:

When the cart is speeding up then its speed is increasing with time hence its acceleration is having a positive value.

• On speeding up the velocity is positive.

• On gradually decreasing the speed and coming to a stop the velocity is still positive with continuously decreasing magnitude until it reaches zero when the cart stops.
• When the cart speeds up in the opposite direction then the velocity of the cart becomes negative from zero and continuously increases in the negative value over a span of time hence its acceleration is also negative.