Nathaniel is driving his sports car down a four lane highway at 40m/s. He comes up behind a slow moving dumptruck and decides to pass it in the left hand lane. If Nathaniel can accelerate at 5m/s^2, how long will it take for him to reach the speed of 60m/s?

Just use the definition of acceleration.

Time required
= (Speed change)/(acceleration)
= (20 m/s)/(5 m/s^2) = 4 s

To find out how long it will take for Nathaniel to reach a speed of 60m/s, we can use the equation of motion:

v = u + at

where:
v is the final velocity (60 m/s)
u is the initial velocity (40 m/s)
a is the acceleration (5 m/s^2)
t is the time we want to find

First, let's rearrange the equation to solve for time (t):

t = (v - u) / a

Now let's substitute the given values into the equation:

t = (60 m/s - 40 m/s) / 5 m/s^2

t = 20 m/s / 5 m/s^2

t = 4 s

Therefore, it will take Nathaniel 4 seconds to reach a speed of 60m/s.

To calculate the time it will take for Nathaniel to reach a speed of 60 m/s, we can use the formula:

Time = (Final Speed - Initial Speed) / Acceleration

Given:
Initial speed, u = 40 m/s
Final speed, v = 60 m/s
Acceleration, a = 5 m/s^2

Plugging the given values into the formula, we get:

Time = (60 m/s - 40 m/s) / 5 m/s^2

Simplifying the equation:

Time = 20 m/s / 5 m/s^2

Dividing the numerator and denominator:

Time = 4 seconds

Therefore, it will take Nathaniel 4 seconds to reach a speed of 60 m/s.