Part 1:
A car accelerates uniformly in a straight line
from rest at the rate of 2.2 m/s2.
What is the speed of the car after it has
traveled 52 m?
Answer in units of m/s.
the answer is 15.126
Part 2:
How long does it take the car to travel 52 m?
Answer in units of s.
???
6.8754545454545
Use
v²-u² = 2aS
where S=distance travelled
a=acceleration
u=initial velocity
v=final velocity
(the given answer is correct)
Use
v=u+at
(the given answer is also correct)
Part 1: To find the speed of the car after it has traveled 52 m, we can use the formula for uniformly accelerated motion:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity (in this case, 0 m/s since the car starts from rest), a is the acceleration, and s is the distance traveled.
Plugging in the given values:
v^2 = (0 m/s)^2 + 2 * (2.2 m/s^2) * (52 m)
v^2 = 0 m/s + 114.4 m^2/s^2
v^2 = 114.4 m^2/s^2
To find v, we take the square root of both sides:
v = sqrt(114.4 m^2/s^2)
v ≈ 10.692 m/s
So, the speed of the car after it has traveled 52 m is approximately 10.692 m/s.
Part 2: To find the time it takes for the car to travel 52 m, we can use another formula for uniformly accelerated motion:
s = ut + 0.5at^2
where s is the distance, u is the initial velocity, a is the acceleration, and t is the time.
Plugging in the given values:
52 m = (0 m/s) * t + 0.5 * (2.2 m/s^2) * (t^2)
52 m = 0 + 1.1 m/s^2 * t^2
Rearranging the equation:
0.55 t^2 = 52 m
Now, we can solve for t by isolating t:
t^2 = 52 m / 0.55 m/s^2
t^2 = 94.545 s^2
Taking the square root of both sides:
t ≈ sqrt(94.545 s^2)
t ≈ 9.72 s
So, it takes approximately 9.72 seconds for the car to travel 52 m.