A CAR ACCELERATES TO 36M/S FOR 4 SECS BEFORE DECELERATING TO 32M/S FOR THE NEXT 6 SECS. CALCULATE THE DISTANCE
PLEASE PLEASE HELP
v=a1•t => a=v/t =36/4 = 9 m/s²
s=at²/2=9•4²/2 =72 m.
v1=v-a1•t1
a1=(v-v1)/t1=(36-32)/6 =0.67.
s1=v•t1-a1•t1²/2 =36•6-(0.67•0.67)/2 =215.9 m.
S = s+s1 =72+215.9 = 287.9 m
Mistake!!!
s1=v•t1-a1•t1²/2 =
=36•6-(0.67•6²)/2 =203.94 m.
S = s+s1 =72+203.94 = 275.94 m
It is more accurate to work with fractions. The above calculations are correct except for minor rounding errors.
We also have to assume that the car started from rest, which was unfortunately not mentioned in the question.
If (2/3) had been used in place of 0.67, we would have got total distance = 276 m
To calculate the distance traveled by the car, you need to calculate the distance traveled during acceleration and deceleration separately, and then add them together.
First, let's calculate the distance traveled during acceleration:
Using the formula: distance = (initial velocity * time) + (0.5 * acceleration * time^2)
The initial velocity (u) during acceleration is 0 m/s,
The final velocity (v) during acceleration is 36 m/s,
The time (t) taken for acceleration is 4 seconds,
And the acceleration (a) is unknown.
Since we have the initial velocity, final velocity, and time, we can use the formula: acceleration = (v - u) / t.
Substituting the values, we have: acceleration = (36 m/s - 0 m/s) / 4 s = 9 m/s^2
Now, let's calculate the distance traveled during acceleration:
distance_acceleration = (0 * 4) + (0.5 * 9 * (4^2)) = 0 + (0.5 * 9 * 16) = 72 meters
Now, let's calculate the distance traveled during deceleration:
Using the same formula: distance = (initial velocity * time) + (0.5 * acceleration * time^2)
The initial velocity during deceleration is 36 m/s (from the last velocity reached during acceleration),
The final velocity during deceleration is 32 m/s,
The time taken for deceleration is 6 seconds,
And the acceleration during deceleration is unknown.
Again, we can use the formula: acceleration = (v - u) / t.
Substituting the values, we have: acceleration = (32 m/s - 36 m/s) / 6 s = -2 m/s^2 (negative due to deceleration)
Now, let's calculate the distance traveled during deceleration:
distance_deceleration = (36 * 6) + (0.5 * (-2) * (6^2)) = 216 + (-36) = 180 meters
Finally, let's add up the distance traveled during acceleration and deceleration:
total_distance = distance_acceleration + distance_deceleration = 72 + 180 = 252 meters
Therefore, the car travels a distance of 252 meters.