A car moving 30m/s slows uniformly to a speed of 10 m/s in a time of 5 sec determine
1) the acceleration of the car
2) the distance it moved in 3 sec
correct answer
a = -4 m/s^2
s = 72 m
Soln to a) a=V-U/t=10-30/5=-4m/s^2 Soln to b) S1= ut+1/2at^2=30*3+1/2*-4*3*3=72m ,t=5-3=2 S2=ut+1/2at^2=10*2+1/2*-4*2*2=52m so, ST= S1+S2=72+52=124m
To answer your questions, we need to use the equations of motion. Specifically, we can use the equation of uniformly accelerated motion, which relates initial velocity (u), final velocity (v), acceleration (a), and time (t). The equation is:
v = u + at
Where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time
Let's calculate:
1) To find the acceleration of the car, we can rearrange the equation by isolating the acceleration term (a):
v = u + at
Rearranging the equation, we get:
at = v - u
Substituting the given values:
v = 10 m/s
u = 30 m/s
t = 5 sec
We can calculate the acceleration using the formula:
a = (v - u) / t
Plugging in the values, we have:
a = (10 - 30) / 5
a = -20 / 5
a = -4 m/s²
Therefore, the acceleration of the car is -4 m/s² (negative because it's slowing down).
2) To find the distance the car moved in 3 seconds, we can use another equation of motion. The equation is:
s = ut + (1/2)at²
Where:
- s is the distance
- u is the initial velocity
- t is the time
- a is the acceleration
To find the distance, we need the initial velocity, but it is not given in this question. However, assuming the car started from rest (u = 0), we can simplify the equation:
s = (1/2)at²
Substituting the given values:
a = -4 m/s²
t = 3 sec
We can calculate the distance using the formula:
s = (1/2)at²
Plugging in the values, we have:
s = (1/2)(-4)(3)²
s = (-2)(9)
s = -18 m
Therefore, the car moved a distance of -18 meters in 3 seconds (negative because it moved in the opposite direction).
since v decreased by 20m/s in 5 sec, a = -4 m/s^2
assuming the 3 seconds started at t=0,
s = 30t - 2t^2
s(3) = 30(3) - 2(9) = 72m