How
long
would
it
take
a
car
that
starts
from
rest
and
accelerates
uniformly
in
a
straight
line
at
5
m/s
2
to
cover
a distance
of
400
m?
After fixing your post:
How long would it take a car that starts from rest and accelerates uniformly in a straight line at 5 m/s^2 to cover a distance of 400 m?
a = 5
v = 5t + c
given: when t = 0, v = 0 , -----> c = 0
v = 5t
s = (5/2)t^2 + k
given: when t = 0 , s = 0 , -----> k = 0
s = (5/2)t^2
then 400 = (5/2)t^2
5t^2 = 800
t^2 = 160
t = √160 = 4√10 = appr 12.65
It took 12.65 seconds.
To calculate the time it would take for a car to travel a distance of 400 meters with uniform acceleration of 5 m/s², we can use the equation of motion:
s = ut + 0.5at²
Where:
- s is the distance covered (400 m in this case)
- u is the initial velocity (which is 0 m/s since the car starts from rest)
- a is the acceleration (5 m/s² in this case)
- t is the time taken to cover the distance
Rearranging the equation, we get:
400 = 0 * t + 0.5 * 5 * t²
Simplifying further:
400 = 2.5t²
Dividing both sides by 2.5:
160 = t²
Taking the square root of both sides:
t = √160
Now, calculating the square root of 160, we find that t is approximately 12.65 seconds. Therefore, it would take the car around 12.65 seconds to cover a distance of 400 meters under the given conditions.