A car starting at x = 49 m accelerates from rest at a constant rate of 8.0 m/s2.
(a) How fast is it going after 10 s?
(b) How far has it gone (from x = 0) after 10 s?
(c) What is its average velocity for the interval 0 t 10 s?
NEED HELP!!!
vf=at
b. distance=49+1/2 a t^2
c. avgvelocity=vf/2
Sure! I can help you with that. To answer these questions, we can use the equations of motion and kinematic equations. Let's break it down step by step:
(a) How fast is the car going after 10 seconds?
To find the car's velocity after 10 seconds, we can use the formula: velocity (v) = initial velocity (u) + (acceleration (a) x time (t)). In this case, the car starts from rest, so the initial velocity (u) is 0 m/s.
Using the given values:
u = 0 m/s (initial velocity)
a = 8.0 m/s^2 (acceleration)
t = 10 s (time)
We can substitute these values into the formula to find the velocity (v):
v = u + (a x t)
v = 0 m/s + (8.0 m/s^2 x 10 s)
v = 0 m/s + 80 m/s
v = 80 m/s
So, after 10 seconds, the car would be going at a speed of 80 m/s.
(b) How far has the car gone from x = 0 after 10 seconds?
To find the distance traveled by the car, we can use the formula: distance (s) = initial velocity (u) x time (t) + (0.5 x acceleration (a) x time (t)^2). In this case, the car starts from rest, so the initial velocity (u) is 0 m/s.
Using the given values:
u = 0 m/s (initial velocity)
a = 8.0 m/s^2 (acceleration)
t = 10 s (time)
We can substitute these values into the formula to find the distance traveled (s):
s = u x t + (0.5 x a x t^2)
s = 0 m/s x 10 s + (0.5 x 8.0 m/s^2 x (10 s)^2)
s = 0 m + (0.5 x 8.0 m/s^2 x 100 s^2)
s = 0 m + 0.5 x 8.0 m/s^2 x 100 s^2
s = 0 m + 400 m
s = 400 m
So, after 10 seconds, the car would have traveled a distance of 400 meters from x=0.
(c) What is the average velocity for the interval 0 < t < 10 seconds?
The average velocity can be found by taking the total displacement and dividing it by the total time. In this case, the displacement is 400 m (as calculated in part b) and the total time is 10 s.
Average velocity = total displacement / total time
Average velocity = 400 m / 10 s
Average velocity = 40 m/s
So, the average velocity for the interval 0 < t < 10 s is 40 m/s.
I hope this helps! Let me know if you have any further questions.
Sure, I can help you with that!
(a) To find the speed of the car after 10 seconds, we can use the formula for velocity:
v = u + at,
where
v = final velocity,
u = initial velocity,
a = acceleration, and
t = time.
In this case, the car starts from rest, so the initial velocity (u) is 0 m/s, the acceleration (a) is 8.0 m/s^2, and the time (t) is 10 s. Plugging these values into the equation, we get:
v = 0 + 8.0 * 10 = 80 m/s.
Therefore, the car is going at a speed of 80 m/s after 10 seconds.
(b) To find the distance traveled by the car after 10 seconds, we can use the formula for displacement:
s = ut + (1/2)at^2,
where
s = displacement.
In this case, the initial velocity (u) is 0 m/s, the acceleration (a) is 8.0 m/s^2, and the time (t) is 10 s. Plugging these values into the equation, we get:
s = 0 * 10 + (1/2) * 8.0 * (10^2) = 0 + 0 + 400 = 400 m.
Therefore, the car has traveled a distance of 400 m from x = 0 after 10 seconds.
(c) The average velocity for the interval 0 < t < 10 s can be calculated using the formula:
v_avg = (v + u) / 2,
where
v_avg = average velocity.
In this case, the initial velocity (u) is 0 m/s, the final velocity (v) is 80 m/s. Plugging these values into the equation, we get:
v_avg = (80 + 0) / 2 = 40 m/s.
Therefore, the average velocity of the car for the interval 0 < t < 10 s is 40 m/s.