Waste less time on Facebook — follow Brilliant.
×

Acceleration doesn't matters?

A particle at rest starts moving with acceleration \(a_1\). Until it reaches the speed \(v\), it immediately decelerates with \(a_2\) until it stops. The total time consumed is \(t\). Show that the displacement of the particle is \(\frac{1}{2}vt\).

Note by Christopher Boo
2 years, 10 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

It can also be interpreted as :
Draw the velocity vs time graph of the particle. We need to find the area under the graph which is the area of the triangle which simply is \( \dfrac{1}{2} \times \text{ base } \times \text{ height } = \dfrac{1}{2} \cdot t \cdot v \). This is the required value.

Sudeep Salgia - 2 years, 10 months ago

Log in to reply

Can be easily proved using \(v\) \(Vs\) \(t\) graph

Dinesh Chavan - 2 years, 10 months ago

Log in to reply

The average velocity with first is (0+v)/2=v/2, in second case it is (v+0)/2=v/2 same as first.
So d = (average velocity)*Time.

Niranjan Khanderia - 2 years, 10 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...