A car accelerates uniformly in a straight line

from rest at the rate of 3.7 m/s2
.
What is the speed of the car after it has
traveled 67 m?
Answer in units of m/s
014 (part 2 of 2) 10.0 points
How long does it take the car to travel 67 m?
Answer in units of s

a = 3.7 m/s^2.

d = 67 m.
Vo = 0
V = ?
t = ?

a. V^2 = Vo^2 + 2a*d. Solve for V.

b. d = 0.5a*t^2 = 67 m. Solve for t.

To find the speed of the car after it has traveled 67 m, we can use the formula:

v^2 = u^2 + 2as

Where:
v is the final velocity (speed) of the car
u is the initial velocity (speed) of the car (which is 0 m/s since the car starts from rest)
a is the acceleration of the car (given as 3.7 m/s^2)
s is the distance traveled by the car (which is 67 m)

Let's calculate the speed (v) first:

v^2 = u^2 + 2as
v^2 = 0^2 + 2 * 3.7 * 67
v^2 = 0 + 488.6
v^2 = 488.6
v ≈ √488.6
v ≈ 22.1 m/s

So, the speed of the car after traveling 67 m is approximately 22.1 m/s.

Now, to find the time it takes for the car to travel 67 m, we can use the formula:

s = ut + (1/2)at^2

Where:
t is the time taken by the car to travel the given distance

Let's rearrange the formula to solve for t:

s = ut + (1/2)at^2
67 = (0)t + (1/2)(3.7)(t)^2
67 = 0 + (1/2)(3.7)(t)^2
67 = (1.85)(t)^2
(t)^2 = 67 / 1.85
(t)^2 ≈ 36.22
t ≈ √36.22
t ≈ 6.02 s

So, it takes approximately 6.02 seconds for the car to travel 67 m.