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Chapter 3: Problem 67

The driver of three-wheeler moving with a speed of \(36 \mathrm{~km} / \mathrm{h}\) sees a child standing in the middle of the road and brings his vehicle to rest in \(4.0 \mathrm{~s}\) just in time to save the child. What is the average retarding force on the vehicle? The mass of the three-wheeler is \(400 \mathrm{~kg}\) and the mass of the driver is \(65 \mathrm{~kg}\). (A) \(1162.5 \mathrm{~N}\) (B) \(116.25 \mathrm{~N}\) (C) \(1112 \mathrm{~N}\) (D) None of these

Short Answer

Expert verified
The short answer to the problem is: (A) \(1162.5 \mathrm{~N}\)

Step by step solution

01

Calculate the total mass of the system

First, we need to find the total mass of the system. Since we have the mass of the vehicle (m鈧�) and the mass of the driver (m鈧�), we can find the total mass (M) by adding the two masses. Total mass M = m鈧� + m鈧�
02

Convert the initial speed to m/s

The given speed is in km/h, and we need to convert it to meters per second (m/s) so that we can easily deal with units in our calculations. To convert from km/h to m/s, we need to multiply the given speed by (1000 m / 1 km) and divide by (3600 s / 1 h). \(v_0 = 36 \frac{km}{h} \cdot \frac{1000\,m}{1\,km} \cdot \frac{1\,h}{3600\,s}\)
03

Find the final velocity

Since the vehicle comes to rest, the final velocity (v) of the vehicle will be 0 m/s. v = 0 m/s
04

Calculate the average acceleration

Now, we will calculate the average acceleration (a) of the vehicle using the formula: \(a = \frac{v - v_0}{t}\) We have the values v, v鈧�, and t, so we can find the acceleration.
05

Calculate the average retarding force

Finally, we will find the average retarding force (F) using the formula: F = M * a We have the value of M and a, so we can calculate the value of F. Once we solve the above steps, we will get the answer to the problem, which we can then match with the given options (A, B, C, or D).

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Most popular questions from this chapter

A car of mass \(m\) is being driven on a circular path of radius \(R\). In which of the following circumstances it will not slip ( \(\mu\) is coefficient of friction between surface and road) (A) \(\frac{m v^{2}}{R} \geq \mu m g\) (B) \(\frac{m v^{2}}{R}=4 \mu \mathrm{mg}\) (C) \(\frac{m v^{2}}{R}>m g\) (D) None

A small block of mass \(m\) is placed in a groove carved inside a disc. The disc is placed on smooth horizontal surface and pulled with an acceleration of magnitude \(25 \mathrm{~m} / \mathrm{s}^{2}\) as shown. Find half of the acceleration of block with respect to the disc in \(\mathrm{m} / \mathrm{s}^{2}\) ? (Given \(\sin \theta=\frac{3}{5}, \cos \theta=\frac{4}{5}, g=10 \mathrm{~m} / \mathrm{s}^{2} \quad\) and co-efficient of friction between groove and the block is \(\mu=\frac{2}{5}\) )

A block of mass \(m\) is attached to a massless spring of spring constant \(K\). This system is accelerated upward with acceleration \(a\). The elongation in spring will be (A) \(\frac{m g}{K}\) (B) \(\frac{m(g-a)}{K}\) (C) \(\frac{m(g+a)}{K}\) (D) \(\frac{m a}{K}\)

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Reading of the spring scale in figure (B) (A) \(90 \mathrm{~N}\) (B) \(62.5 \mathrm{~N}\) (C) \(55 \mathrm{~N}\) (D) \(75 \mathrm{~N}\)
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