Question

A locomotive is accelerating at 1.6 m/s2. it passes through a 20.0-m-wide crossing in a time of 2.4 s. after the locomotive leaves the crossing, how much time is required until its speed reaches 32 m/s?

Answer 1

Answer:

After reaching crossing locomotive takes 17.6 seconds to reach velocity 32 m/s.

Explanation:

  Acceleration of locomotive = 1.6 $m/s^2$

  Time at which it crosses crossing = 2.4 seconds.

  We have equation of motion, v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time taken.

  When it reaches 32 m/s, v = 32 m/s, u = 0 m/s, a= 1.6 $m/s^2$ seconds.

   32 = 0 + 1.6 * t

    t = 20 seconds.

  So locomotive's velocity is 32 m/s after 20 seconds and it reaches crossing at 2.4 seconds.

  So after reaching crossing it takes 17.6 seconds to reach velocity 32 m/s.

Answer 2

It required about 14 seconds after the locomotive leaves the crossing until its speed reaches 32 m/s.

Further explanation

Acceleration is rate of change of velocity.

$\large {\boxed {a = \frac{v - u}{t} } }$

$\large {\boxed {d = \frac{v + u}{2}~t } }$

a = acceleration (m / s²)v = final velocity (m / s)

u = initial velocity (m / s)

t = time taken (s)

d = distance (m)

Let us now tackle the problem!

Given:

a = 1.6 m/s²

d = 20.0 m

t₁ = 2.4 s

v₂ = 32 m/s

Unknown:

Δt = ?

Solution:

Initially, we calculate the initial speed of the locomotive when entering the crossing.

$d = ut + \frac{1}{2}at_1^2$

$20 = u(2.4) + \frac{1}{2}(1.6)(2.4)^2$

$20 = u(2.4) + 4.608$

$u(2.4) = 20 - 4.608$

$u = 15.392 \div 2.4$

$u = (481 \div 75) ~ m/s$

Next we calculate the total time needed for the locomotive to reach 32 m/s

$v_2 = u + at_2$

$32 = (481 \div 75) + 1.6t_2$

$t_2 = (32 - \frac{481}{75}) \div 1.6$

$t_2 \approx 16 ~ seconds$

Finally, the time needed for the locomotive to reach a speed of 32 m/s after leaving the crossing is:

$\Delta t = t_2 - t_1$

$\Delta t = 16 - 2.4$

$\Delta t \approx 14 ~ seconds$

Learn more

• Velocity of Runner : brainly.com/question/3813437

• Kinetic Energy : brainly.com/question/692781

• Acceleration : brainly.com/question/2283922

• The Speed of Car : brainly.com/question/568302

Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate , Sperm , Whale , Travel