a car starts from rest and has a constant acceleration of 2.5 m/s^2. if it travels 25m how long will it take to complete the motion
4rm eqns of motion
s=ut + 1/2at^2
since u =0
s=1/2at^2
25=0.5*2.5 *t^2
t^2=25/1.25
t^2=20secs^2
t=4.5secs
To find the time taken to complete the motion, we can use the equations of motion. In this case, we have initial velocity (u) as 0 m/s (since the car starts from rest), acceleration (a) as 2.5 m/s², and distance (s) as 25 m.
The equation that relates these quantities is:
s = ut + (1/2)at²
In this equation, s represents the distance traveled, u is the initial velocity, t is the time taken, and a is the acceleration.
Since the car starts from rest (u = 0), the equation simplifies to:
s = (1/2)at²
Plugging in the given values, we have:
25 = (1/2) * 2.5 * t²
To solve for t², divide both sides by (1/2) * 2.5:
25 / (1/2) * 2.5 = t²
Simplifying further:
25 / (1/2) * 2.5 = 4 * t²
25 / (1/2) = 10 * t²
50 = 10 * t²
Divide both sides by 10:
50 / 10 = t²
5 = t²
To solve for t, take the square root of both sides:
√5 = t
Therefore, the car will take approximately √5 seconds to complete the motion.
Note: The square root of 5 is an irrational number, approximately equal to 2.236.