Question

While traveling along the highway a driver slows from 50m/s to 20 m/s in 10 seconds. What is the driver’s acceleration?

Answer 1

-3
`(m)/(s^2)`

Step-by-step explanation

Acceleration is the rate of change in velocity over time, or how greatly an object speeds up or down per unit of time. This is a vector quantity, so it has both magnitude and direction. Knowing this, we can create an equation for acceleration that shows the relationship between velocity and time.

Since acceleration is change in velocity over time, or per unit of time, we can write this as a = Δv/t.

a represents acceleration in meters per second squared (
`(m)/(s^2)`)

Δv represents change in velocity in meters per second (
`(m)/(s)`)

t represents time in seconds (s)

This is because as each unit of time passes, the velocity changes by the acceleration value. For example, if the acceleration is 2
`(m)/(s^2)`, and the object starts at 5
`(m)/(s)`, one second later, the object will be moving at a velocity of 2 + 5 = 7
`(m)/(s)`.

Note that the change in velocity can also be written as
`v_f-v_o` where
`v_f\\` is the final velocity and
`v_o` is the initial velocity, since the change in velocity is the difference between the initial and final velocities.

So our equation a = Δv/t becomes a =
`(v_f-v_o)/(t)`

Now that we have an equation, we can plug in values and use algebra to solve. In the question the given values are an initial velocity (
`v_o`) of 50
`(m)/(s)`, a final velocity (
`v_f`) of 20
`(m)/(s)`, and a time (t) of 10 seconds.

a =
`(v_f-v_o)/(t)`

a =
`(20-50)/(10)`

a =
`(-30)/(10)`

a = -3
`(m)/(s^2)`

The acceleration of the driver is -3
`(m)/(s^2)`. Note that this value is negative, because the velocity decreases over time. This matches the information in the question that states that the driver slows down. The negative sign indicates the direction of acceleration, which is opposite the direction of motion and velocity. If acceleration were positive, the acceleration would be in the same direction of motion and velocity of the driver. The absolute value of acceleration, | -3 | = 3, indicates the magnitude of acceleration.