When the break are applied to a moving car travelling at 60km/hr at decelerate at a uniform rate of 5m/s^2. .calculate the time taken to reach a velocity of 36km/hr
a = -5 m/s^2
60 km/h = 60000/3600 m/s = 50/3 m/s
36 km/h = 10 m/s
v = at + c
v = -5t + c
at start of event, t = 0, v = 50/3
50/3 = 0+c
so v = -5t + 50/3
solve for t when v = 10 m/s
10 = -5t + 50/3
t = 4/3 seconds
when the breaks are applied to a moving car travelling at 60km/hr at decelerate at a uniform rate of 5m/s^2.calculate the time taken to a reach a velocity of 36km/hr.
4/3
-1.34
To calculate the time taken to reach a velocity of 36 km/hr, assuming a uniform deceleration rate of 5 m/s^2, we can follow these steps:
Step 1: Convert the initial velocity and target velocity from km/hr to m/s.
Initial velocity (u) = 60 km/hr
Target velocity (v) = 36 km/hr
1 km/hr = (1/3.6) m/s
So, initial velocity (u) = 60 km/hr × (1/3.6) m/s = 16.67 m/s
Target velocity (v) = 36 km/hr × (1/3.6) m/s = 10 m/s
Step 2: Use the kinematic equation to calculate the time (t).
The kinematic equation relating initial velocity (u), final velocity (v), acceleration (a), and time (t) is:
v = u + at
Since the car is decelerating, the acceleration (a) will be negative because it is acting opposite to the direction of the velocity.
Substituting the values:
10 m/s = 16.67 m/s + (-5 m/s^2) × t
Simplifying the equation, we have:
10 m/s - 16.67 m/s = -5 m/s^2 × t
-6.67 m/s = -5 m/s^2 × t
Step 3: Solve the equation for time (t).
To solve for t, divide both sides of the equation by -5 m/s^2:
t = (-6.67 m/s) / (-5 m/s^2)
The units of "m/s" cancel out, leaving seconds (s) as the unit for time:
t = 6.67 s
Therefore, it will take approximately 6.67 seconds for the car to reach a velocity of 36 km/hr.