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The deceleration of a car travelling on a straight highway is a function of its instantaneous velocity v given by w=a sqrt v ,where a is a constant.if the initial velocity of the car is 60km/hr the distance the car will travel and the time it takes to stop are?? 1)3/2a m,1/2a s 2)2/3a m,2/a s. (s stands for seconds)
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The deceleration of a car travelling on a straight highway is a functi...
Solution:
Given, w = a sqrt v, where a is a constant.
Initial velocity, u = 60 km/hr = 16.67 m/s (1 km/hr = 5/18 m/s)
Let the final velocity be 0 m/s.
We know that, v^2 = u^2 - 2as
At the point of stopping, v = 0, a = w = a sqrt v
∴ v = a sqrt v
Squaring both sides, we get
v^2 = a^2 v
∴ v = a^2 v / v
a^2 = 1
a = ± 1 (since a is a positive constant, we take a = 1)
Now, w = a sqrt v = sqrt v
Given, w = dw/dt = a sqrt v
∴ dw/dt = sqrt v
Integrating both sides, we get
∫dw = ∫sqrt v dt
w = (2/3)v^(3/2) + C1
At t = 0, w = a sqrt v
∴ C1 = -2/3
Therefore, w = (2/3)(v^(3/2) - sqrt v)
At the point of stopping, v = 0, w = a sqrt v = 0
∴ (2/3)(0 - 0) = (2/3)(u^(3/2))
∴ u^(3/2) = 0
∴ u = 0
The car will not stop at all as the initial velocity is 16.67 m/s and the final velocity should be 0 m/s.
Hence, the given options are incorrect.
Note: The problem statement may have some errors, as the car cannot stop with the given initial velocity and the given function for deceleration.
Given, w = a sqrt v, where a is a constant.
Initial velocity, u = 60 km/hr = 16.67 m/s (1 km/hr = 5/18 m/s)
Let the final velocity be 0 m/s.
We know that, v^2 = u^2 - 2as
At the point of stopping, v = 0, a = w = a sqrt v
∴ v = a sqrt v
Squaring both sides, we get
v^2 = a^2 v
∴ v = a^2 v / v
a^2 = 1
a = ± 1 (since a is a positive constant, we take a = 1)
Now, w = a sqrt v = sqrt v
Given, w = dw/dt = a sqrt v
∴ dw/dt = sqrt v
Integrating both sides, we get
∫dw = ∫sqrt v dt
w = (2/3)v^(3/2) + C1
At t = 0, w = a sqrt v
∴ C1 = -2/3
Therefore, w = (2/3)(v^(3/2) - sqrt v)
At the point of stopping, v = 0, w = a sqrt v = 0
∴ (2/3)(0 - 0) = (2/3)(u^(3/2))
∴ u^(3/2) = 0
∴ u = 0
The car will not stop at all as the initial velocity is 16.67 m/s and the final velocity should be 0 m/s.
Hence, the given options are incorrect.
Note: The problem statement may have some errors, as the car cannot stop with the given initial velocity and the given function for deceleration.
Community Answer
The deceleration of a car travelling on a straight highway is a functi...
Bro do u have solution for this
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The deceleration of a car travelling on a straight highway is a function of its instantaneous velocity v given by w=a sqrt v ,where a is a constant.if the initial velocity of the car is 60km/hr the distance the car will travel and the time it takes to stop are?? 1)3/2a m,1/2a s 2)2/3a m,2/a s. (s stands for seconds)
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