1.
A European sports car dealer claims that his product will accelerate at a constant rate from rest to a speed of 81 km/hr in 10 seconds. What is the speed after the first 7 seconds of acceleration?
A) 157.5 m/s
B) 22.5 m/s
C) 56.7 m/s
D) 15.8 m/s
E) 32.1 m/s
Obviously, first convert to m/s.
yes convert km/hr to m/s.
Then acceleration is deltaV/time
speed= a*7
To convert the speed from km/hr to m/s, you can use the conversion factor 1 km/hr = 0.278 m/s.
So, the speed of 81 km/hr can be converted to m/s as follows:
81 km/hr x 0.278 m/s = 22.518 m/s (rounded to three decimal places).
Now, let's find the acceleration using the given information that the car accelerates at a constant rate.
Acceleration is defined as the change in velocity divided by the time taken.
Initial velocity (u) = 0 m/s (since the car starts from rest)
Final velocity (v) = 22.518 m/s (after 10 seconds of acceleration)
Time (t) = 10 seconds
Using the formula:
Acceleration (a) = (v - u) / t
a = (22.518 m/s - 0 m/s) / 10 seconds
a = 2.2518 m/s^2
Now, to find the speed after the first 7 seconds of acceleration, we use the formula:
Final velocity (v) = Initial velocity (u) + (Acceleration (a) x Time (t))
Final velocity (v) = 0 m/s + (2.2518 m/s^2 x 7 seconds)
Final velocity (v) = 15.761 m/s
Therefore, the speed after the first 7 seconds of acceleration is approximately 15.761 m/s.
So, the correct answer is D) 15.8 m/s.
To convert from kilometers per hour (km/hr) to meters per second (m/s), you need to use the conversion factor of 1 km/hr = 0.2778 m/s.
So, the speed of 81 km/hr can be converted to m/s by multiplying it by 0.2778:
81 km/hr * 0.2778 m/s = 22.5 m/s
Therefore, the speed of the car is 22.5 m/s after accelerating for 10 seconds.
Next, to find the speed after the first 7 seconds of acceleration, you need to use the concept of constant acceleration.
The formula to calculate speed with constant acceleration is:
v = u + at
where:
- v is the final velocity (speed)
- u is the initial velocity (in this case, the speed at rest is 0 m/s)
- a is the acceleration
- t is the time
Since the car starts from rest, the initial velocity (u) is 0 m/s. The acceleration (a) is constant throughout, as stated in the problem. And the time (t) given is 7 seconds.
So, the formula becomes:
v = 0 + a * 7
You need to know the acceleration in order to solve this problem. However, the problem statement only mentioned the time and final velocity, not the acceleration. Therefore, it is impossible to determine the speed after the first 7 seconds of acceleration with the given information.
Thus, the answer is indeterminable.