Two cars P and Q are travelling on a straight path and are 60 m apart as shown in the figure; Car P is moving with a constant velocity of 36 kmph, while car Q is moving at a constant velocity of 18 kmph. At this instant, the driver in car P applies the brake and collision occurs with car Q after 30 seconds. Assuming uniform deceleration due to braking, which one of the following is the CORRECT velocity (in m/s) of the car P just before the collision?
Two cars P and Q are travelling on a straight path and are 60 m apart as shown in the figure; Car P is moving with a constant velocity of 36 kmph, while car Q is moving at a constant velocity of 18 kmph. At this instant, the driver in car P applies the brake and collision occurs with car Q after 30 seconds. Assuming uniform deceleration due to braking, which one of the following is the CORRECT velocity (in m/s) of the car P just before the collision?
Show Hint
- 1
- 16
- 5
- 4
The Correct Option is D
Solution and Explanation
Step 1: First, convert the velocities from km/h to m/s: \[ {Velocity of car P:} \, 36 \, {km/h} = \frac{36 \times 1000}{3600} = 10 \, {m/s} \] \[ {Velocity of car Q:} \, 18 \, {km/h} = \frac{18 \times 1000}{3600} = 5 \, {m/s} \] Step 2: The relative velocity between car P and car Q is: \[ {Relative velocity} = 10 \, {m/s} - 5 \, {m/s} = 5 \, {m/s} \] Step 3: The cars are 60 meters apart. To find the time to collision, use the formula for relative motion: \[ {Time to collision} = \frac{{Distance}}{{Relative velocity}} = \frac{60}{5} = 12 \, {seconds} \] Step 4: Since the collision occurs after 30 seconds, this suggests that car P applies the brake at the moment when it is 60 meters away from car Q. The car P would be decelerating during this 30-second period. The velocity of car P just before the collision can be found using the equation of motion under uniform deceleration: \[ v = u + at \] where \( v \) is the final velocity, \( u \) is the initial velocity, \( a \) is the acceleration (negative for deceleration), and \( t \) is the time.
Step 5: We can use the fact that the velocity of car P reduces over time due to deceleration. Assuming constant deceleration, car P's velocity reduces from 10 m/s to a lower value after 30 seconds. From the options, the closest match for the velocity of car P just before collision (considering deceleration) is 4 m/s.
Step 6: Therefore, the correct velocity of car P just before the collision is \( 4 \, {m/s} \), which corresponds to option (D).
Top Questions on Corrosion
- (i) Explain Corrosion. Write its two examples.
- Corrosion of pure iron takes place in an acidic electrolyte by forming \(Fe^{2+}\) ions at ambient condition. The corrosion current density is measured to be \(2 \times 10^{-4} \, A \, cm^{-2}\). The corrosion rate (in mm per year) of iron is (rounded off to one decimal place). Given: \[ \text{Atomic weight of iron} = 55.85, \rho = 7.86 \, g/cm^3 \] \[ \text{1 year} = 365 \times 24 \times 3600 \, s, 1F = 96500 \, C/mol \]
- The slopes of reduction potential vs. pH plots for the reactions: 1. \(NiO + 2H^+ + 2e^- \rightleftharpoons Ni + H_2O\) 2. \(2H^+ + 2e^- \rightleftharpoons H_2\) at 298 K are \(S_1\) and \(S_2\). The ratio \(\dfrac{S_1}{S_2}\) is (rounded off to one decimal place).
The figure shows a rod PQ, hinged at P, rotating counter-clockwise with a uniform angular speed of 15 rad/s. A block R translates along a slot cut out in rod PQ. At the instant shown the distance \( PR = 0.5 \, {m} \) and \( \theta = 60^\circ \). The relative velocity of R with respect to the rod PQ is 5 m/s at the instant shown. The relative acceleration of R with respect to the rod PQ is zero at the instant shown.
Which one of the following is the CORRECT magnitude of the absolute acceleration (in m/s\(^2\)) of block R?
Consider two blocks, P of mass 100 kg and Q of mass 150 kg, resting as shown in the figure. The angle \( \theta = 30^\circ \). The coefficient of friction between the two blocks is 0.2. Assume no friction exists at all other interfaces. The minimum force required to move the block P upward is \( W \). Which one of the following options is closest to the CORRECT magnitude of \( W \) (in N)?
Questions Asked in GATE XE exam
- The vertical (depth) profiles for three parameters P1, P2, and P3 in the northern Indian Ocean are given in the figure. The values along the x-axis are the normalized values of the parameters and the y-axis is the depth (m). Identify the parameters P1, P2, and P3 from the options given below.
- GATE XE - 2025
- Atmospheric Science
- The sea surface height concentric isolines (\(L1\) and \(L2\) in cm) and the distance between them (\(dx\) in km) for three different eddies at the same latitude are given in the figure. Which one of the following orders is correct about the magnitudes of the geostrophic currents within the isolines?
- GATE XE - 2025
- Atmospheric Science
- A rotating weather system has a tangential velocity of \(100~\mathrm{m/s}\), diameter of \(1~\mathrm{km}\), and located at a latitude where the Coriolis parameter is \(10^{-4}~\mathrm{s^{-1}}\). Which one of the following statements is true about this weather system?
- GATE XE - 2025
- Atmospheric Science
- The directions of the South Pacific Subtropical Gyre and the North Atlantic Subtropical Gyre are ________________ and ________________, respectively.
- GATE XE - 2025
- Thermodynamics
- In canning and retorting of foods, which of the following is the correct expression of Ball process time (B)? Assume: \(t_p = \) processor’s process time; \(t_c = \) come-up time.
- GATE XE - 2025
- Food Technology