Q 13. - Calculus

Question

Suppose v(t) is the velocity of a particle moving on a straight path, where v is measured in meters per second and t is measured in seconds. The particle starts moving

at time $t_0$ and moves for $∆t$ seconds.

(a) What are the units of $v\left(t_0\right)∆t$?

(b) Geometrically, what does $v\left(t_0\right)∆t$ represent?

(c) What do these questions have to do with this section?

Step-by-Step Solution

Answer

(a) Meters

(b) Area of the rectangle

(c) Distance is related to the area under the velocity curve.

Step 1. Given information

v(t) is the velocity of a particle moving on a straight path, where v is measured in meters per second and t is measured in seconds. The particle starts moving at time $t_0$ and moves for $∆t$ seconds.

Step 2. Explanation

v(t) is the velocity of a particle moving on a straight path, where v is measured in meters per second and t is measured in seconds. The particle starts moving at time $t_0$ and moves for $∆t$ seconds.

(a) Units of $v\left(t_0\right)∆t$ is meters.

(b) $v\left(t_0\right)∆t$ represents the area of a rectangle.

(c) This section denotes that distance is related to the area under the velocity curve.