An automobile travelling with a speed of 60km/hr, can apply brake to stop within a distance
of 20m. If the car is going twice as fast then calculate the stopping distance and stopping time?
(b) Given R1 = 5.0 ± 0.2 and R2 = 10.0 ± 0.1. calculate the total resistance in parallel with possible
% error?
a. The stopping distance is proportional to the square of the initial velocity:
Ds = 2^2 * 20m = 80m = Stopping distance.
The stopping time is proportional to the initial velocity:
Vo = 60000m/h * (1h/3600s) = 16.67m/s.
a = (Vf^2-Vo^2) / 2d,
a = (0-(16.67)^2 / 40 = 6.94m/s.
Ts = (vF-2Vo) / A,
tS = (0 - 33.33) / -6.94 = 4.80s.
b. Do you mean +-0.2% and +-0.1%?
32
1346-
To calculate the stopping distance and stopping time, we need to use the equation for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Since the velocity of the car is given as 60 km/hr, we need to convert it to m/s:
Velocity = 60 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 16.67 m/s
The stopping distance is given as 20 m. To calculate the stopping time, we can use the equation:
Stopping Distance = (1/2) * acceleration * stopping time^2
Since we want to calculate the stopping time, we rearrange the equation:
stopping time = sqrt((2 * stopping distance) / acceleration)
Now, we substitute the given values into the equation:
stopping time = sqrt((2 * 20 m) / acceleration)
To calculate acceleration, we can use the equation:
acceleration = (final velocity^2 - initial velocity^2) / (2 * stopping distance)
In this case, the initial velocity is 0 m/s, and the final velocity is twice the initial velocity (2 * 16.67 m/s).
Now, we substitute the values and solve for acceleration:
acceleration = (2 * (2 * 16.67 m/s)^2) / (2 * 20 m)
Next, we substitute the value of acceleration back into the equation for stopping time:
stopping time = sqrt((2 * 20 m) / acceleration)
By substituting the values and evaluating the equation, we can find the stopping time.
To calculate the total resistance in parallel and the possible % error, we use the formula:
1/Total Resistance = 1/R1 + 1/R2
Substituting the given values:
1/Total Resistance = 1/5.0 ± 0.2 + 1/10.0 ± 0.1
Add the fractions and calculate the reciprocal to obtain the total resistance. Then, we calculate the error % as follows:
Error % = (Absolute error / Total resistance) * 100
Substitute the values and calculate the error %.