A cart has a constant acceleration of a = 2m/s2. At a certain instant its speed is 5 m/s. What is its speed 2 s later and 2 s earlier?. What is its average speed during the time interval of 4s.?
sadas
Well, well, well, let's calculate the speed of this cart and have some fun with it!
If the acceleration of the cart is a steady 2 m/s², then we can use the good ol' kinematic equations to crack this puzzle!
Firstly, let's find the speed of the cart 2 seconds later. We can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Plugging in the values we have, v = 5 m/s + 2 m/s² * 2 s = 9 m/s. Voila!
Now, onto the speed 2 seconds earlier. We can use the same formula, but this time we need to subtract the product of acceleration and time. So, v = 5 m/s - 2 m/s² * 2 s, which gives us v = 1 m/s. That cart was really slowing down!
Lastly, let's find the average speed during the 4-second time interval. The average speed is simply the total distance traveled divided by the total time taken. However, since we don't have the distance, let's use another handy equation: v = u + at. Rearranging it, we get v = u + a(t - t₀), where t₀ is the initial time.
In this case, the initial time is 2 seconds earlier, so t₀ = -2 s. Plugging in the values, we have v = 5 m/s + 2 m/s²(4 s - (-2 s)). Simplifying that, we get v = 5 m/s + 2 m/s² * 6 s = 17 m/s.
So, the average speed during the 4-second interval is a whopping 17 m/s. That cart was really zooming around!
Hope that answers your question and brings a smile to your face!
To find the speed of the cart 2 seconds later, we can use the formula:
v = u + at
Where:
v = final velocity (speed)
u = initial velocity (speed)
a = acceleration
t = time
Given that the acceleration (a) is 2 m/s² and the initial velocity (u) is 5 m/s, we can substitute these values into the formula:
v = 5 m/s + 2 m/s² * 2 s
Simplifying the equation:
v = 5 m/s + 4 m/s
v = 9 m/s
Therefore, the speed of the cart 2 seconds later is 9 m/s.
To find the speed of the cart 2 seconds earlier, we can use the same formula:
v = u + at
Given that the acceleration (a) is 2 m/s² and the initial velocity (u) is 5 m/s, we can substitute these values into the formula:
v = 5 m/s + 2 m/s² * (-2 s)
Simplifying the equation:
v = 5 m/s - 4 m/s
v = 1 m/s
Therefore, the speed of the cart 2 seconds earlier is 1 m/s.
To find the average speed during the time interval of 4 seconds, we can use the formula:
Average speed = (final speed + initial speed) / 2
Given that the final speed is 9 m/s and the initial speed is 1 m/s, we can substitute these values into the formula:
Average speed = (9 m/s + 1 m/s) / 2
Simplifying the equation:
Average speed = 10 m/s / 2
Average speed = 5 m/s
Therefore, the average speed during the time interval of 4 seconds is 5 m/s.
To find the speed of the cart 2 seconds later and 2 seconds earlier, we can use the kinematic equation:
v_t = v_0 + at
where
v_t is the final velocity (speed) at time t,
v_0 is the initial velocity (speed) at time 0,
a is the constant acceleration, and
t is the time elapsed.
Let's find the speed 2 seconds later first. Given that the initial velocity v_0 is 5 m/s and the acceleration a is 2 m/s²:
v_t = v_0 + at
v_t = 5 m/s + (2 m/s²)(2 s)
v_t = 5 m/s + 4 m/s
v_t = 9 m/s
So the speed of the cart 2 seconds later is 9 m/s.
Now let's find the speed 2 seconds earlier. We'll use the same formula, but this time the time t will be negative (-2 s):
v_t = v_0 + at
v_t = 5 m/s + (2 m/s²)(-2 s)
v_t = 5 m/s - 4 m/s
v_t = 1 m/s
Therefore, the speed of the cart 2 seconds earlier is 1 m/s.
To find the average speed during the time interval of 4 seconds, we need to know the initial and final velocities. From the given information, we know the initial velocity v_0 is 5 m/s. To find the final velocity v_f, we can use the equation:
v_f = v_0 + at
Given that the acceleration a is 2 m/s² and the time t is 4 seconds, we can calculate the final velocity:
v_f = 5 m/s + (2 m/s²)(4 s)
v_f = 5 m/s + 8 m/s
v_f = 13 m/s
The average speed during the 4-second interval is calculated by finding the total distance traveled (which is equal to the displacement since acceleration is constant) and dividing it by the time:
average speed = total distance / total time
average speed = (displacement) / (4 s)
Since the acceleration is constant, the displacement can be determined using the equation:
displacement = (v_f + v_0) / 2 * t
displacement = (13 m/s + 5 m/s) / 2 * 4 s
displacement = 18 m/s / 2 * 4 s
displacement = 9 m/s * 4 s
displacement = 36 m
Now, let's calculate the average speed:
average speed = 36 m / 4 s
average speed = 9 m/s
Therefore, the average speed during the time interval of 4 seconds is 9 m/s.