A driver of a car traveling at 17.1 m/s applies the brakes, causing a uniform deceleration of 1.5 m/s2.
How long does it take the car to accelerate to a final speed of 13.3 m/s?
Answer in units of s
I know that there are simple physics formulas for this, but I like doing these using simple Calculus.
we are given
a = -1.5 m/s^2 , then
v = -1.5t + c
given: when t=0, v = 17.1
17.1 = 0 + c, c = 17.1, so
v = -1.5t + 17.1
when v = 13.3 ...
13.3 = -1.5t + 17.1
1.5t = 3.8
t = 3.8/1.5 = 2.53 seconds
To find the time it takes for the car to accelerate to a final speed, we can use the equation of motion:
v = u + at
Where:
v is the final velocity (13.3 m/s)
u is the initial velocity (17.1 m/s)
a is the acceleration (-1.5 m/s^2) since it's a deceleration
t is the time we want to find
Rearranging the equation to solve for time:
t = (v - u) / a
Substituting the given values:
t = (13.3 - 17.1) / (-1.5)
Now we can calculate the time:
t = (-3.8) / (-1.5)
t = 2.53 seconds
Therefore, it takes approximately 2.53 seconds for the car to accelerate to the final speed of 13.3 m/s.